Transmutation in Alchemical sense means making something more perfect.
Following your logic, when you become old, your own limbs will start defying you and mind will be deteriorating to your own displeasure, will you still be calling it "transmutation"?
If you are going to say that it is period when your wisdom reaches its peak, well, there are syndrome of Alzheimer, syndrome of Parkinson and many other syndromes and pathologies which most of the modern people experience during old age, and all of them point at rather degradation of their "wisdom" and "knowledge" than anything else.
That was exactly the point in example in OP, when old people didn't want to live any more. There is little point when your own body and mind are disobeying you: you are not beautiful, you are not wise, you are not healthy, you are in state of degradation.
What concerns Tholde and Valentine, there are many such stories with other alchemists too: with Fulcanelli, with Eireneus Philalethes, etc. This world is full of deception, it is hard to separate truth from lie, they constatnly go intertwined with each other in this world, but sometimes you can find surprising gems of wisdom where you least expect it.
Making something more perfect is subjective and arbitrary based upon the current experience level of the observer. Transmutation is about a change-in-state, growth and evolution from one thing to another, metamorphosis.
Following your logic the description of old age you have given is more about disease than ageing. People suffering from the conditions you have outlined are victims of physical and mental deterioration caused by many variables some of which can be eliminated by behavior changes. If you do not eliminate them then you will suffer the misery of old age diseases and lose your body matter to tiny predators and recyclers.
You will get older and the feces of living will clog your circulatory systems until the obstructions initiate the symptoms of old age diseases ending in death as usual. Alchemists work to remove such feces through their medicines and meditations derived through them.
You miss the point of the metaphor of the infant and child. The physical body will eventually ware out no matter what. It will not be able to carry you further just like the infant and child bodies were not able to carry you further in your continuing metamorphosis. You left them behind and will do the same with the physical body sooner or later depending upon how much you Know, and what you are Willing to Dare in the Silence.
The Taoist alchemists have maintained that besides the physical body we have a subtle body that will outlast the physical one into thousands of years. It will not last at all if you are unaware of it and never exercise the circulations it requires. It will give up the Ghost same as the physical body when it dies. Then the Ghost gets recycled in the MicroCosmic Egg.
This sounds quite fanciful to one not initiated into the Inner Circulation of Light or Qi as taught by the Taoists. To become aware of the Inner Circulation requires repetitive exercises like taught in various Chinese Inner Alchemy practices. One has to achieve at least this basic experience and knowledge to exercise one's own Inner Circulation. From that success arises the potential of giving birth to your Immortal Fetus.
That newly born subtle body is an infant at first then a child and so on until you can operate it to advantage just like you did with your physical body. It takes time and exercise to evolve. If your physical body craps out on you before the subtle one is sufficiently developed then the Ghost gets recycled.
Alchemist and Philosopher Roger Bacon addressed the subject of long life and immortality nearly 800 years ago:
Of Old Age, and Long Life: Chap. VII:
Of Retarding the Accidents of Old Age, and Prolongation of Life.
The furthest attainment, which the complement of Art, joyned with the whole Energy of Nature can reach unto, is the Prolongation of Life to a very old date. How farre this is attainable, manifold experience has shewed us. Pliny reports, That Pellio, a man of strong body and mind, lived much longer then men usually now, of whom OEtavius Augustus enquiring, What course he took to live so long? Was answered aenigmatically, he used Oyl without, and Mulsum within (now according to the opinion of some, it’s eight parts of water, and nine of honey) I might produce many examples of the same quality: as that which fell out in the days of King William; A Countreyman plowing in the field, found a golden vessel, containing a certain liquor, which he supposing to be the Dew of Heaven, washed his face withal, and drunk of it, whereby he became renued in spirit, body and excellence, from a Plow-man he was made a Porter to the King of Sicily. And the Popes Letters assures us, That Almannus, held Prisoner by the Saracens, through the use of a Medicine lived five hundred years. For the King, whose Captive he was, having received the Medicine from the Embassadours of the great King, and being suspitious of them, made trial hereof upon his Captive, which was brought him for that purpose. And the Lady of the Woods in great Britanny searching for a white Hind, found an Olinment, wherewith the Keeper of the Woods anointed his whole body, except the soals of his feet, and he lived three hudred years without any corruption, save in the soals of his feet, which had some passions. We ourselves know it frequent in these days, That plain Countrey men without the advantage so much as of a Physicians advice, live very healthfully an hundred years, or little less. And these are rather confirmed by the operations of Animals, as Harts, Eagles, Serpents, and many others, who by the efficacy of heart or stones, have renewed their youth: And wise men seeing that even bruits could reach so farre to their Prolongation, adjudging it no less feasible by reasonable men, set themselves on the Spurre to find out this secret. Hereupon Artefius from his own ingenuity, having found the Secrets of Stones, Herbs, Sensibles , & c. both for the knowledge of Nature, and especially the Prolongation of Life, did rejoice, that he had lived 1025 yeares. Further, to confirme this Assertion of the Prolongation of Life, it’s considerable, that man naturally is immortal, that is to say, has the possibility of not dying. Yea, even after his fall, he might live a thousand years, though by degrees the length of life was abbreviated. Hence it follows, That this abbreviation is Accidental, and consequentially may be repaired in whole or in part; and upon search we shall find the accidental cause of the corruption, is not from the Heavens, or any other than the defect of true Government of our health. In that our Fathers are corrupt and imbecile, they beget sonnes of a corrupt complexion and composition, and their children upon the same score are corrupted. Thus the Pedigree of corruption is deprived from Fathers to sonnes, until we settle upon our heirs an assured abbreviation of our dayes. Yet this doth not conclude, That to perpetuity there shall succeed an abbreviation of our life, since there is a positive period set to our life, men may live till they be eighty years, though then their dayes be but labor and sorrow.
Now if every man would from the brest exercise a compleat Regiment of heath (which consists in such things as have relation to Meat, Drink, Sleep, Waking, Motion, Rest, Evacuation, Retention, Air, and the Passions of the mind) He might find a remedy resisting his proper malady. For upon the prosecution of such a Regiment, one might arrive at the uttermost limit of that Nature he had from his Parents will permit, and be led to the very last period of Nature (I mean Nature fallen from its original uprightness) beyond which there is no further progress; because it doth little or nothing availe against the corruption of our Ancestours: and yet the fore-mentioned things, as the Regiment of health exacts, wherefore abbreviation of our dayes does not only from our Progenitors, but hath its advantages from the want of Regiment. However the Art of Physick sufficiently determines this. Although nor rich, or poor, wise or ignorant, no nor the most accurate Physicians themselves, do accomplish this Regiment in themselves or others, as every eye can descern. Yet Nature is not deficient in Necessaries or Art any wayes incompleat, but rather is advantagious to make insurrections and irruptions against, and so farre into these accidental passions, as they are either whole or in part rooted out. At first, and in the beginning of our ages declining, the remedy was easie: But since we have five thousand years or more disadavantage, the Cure is more craggy.
But waving the Inconveniences wise men moved by the considerations formentioned, have endeavoured to find out the means and wayes, which not only are forceable against the defects of every mans proper Regiment, but also agains the corruptions of our Parents; Not that hereby they can attain to the years of Adam or Artefius, by reason of the growing corruption, but our dayes may be augmented an hundred years or more, above the ordinary age of most men in these dayes. And though it be impossible absolutly to retard the accidents of old age, yet hereby they may mitigate them, so as life will happily be prorogued beyond the common account, yet alwayes within the ultimate circuit of Nature. There is a bounder of Nature, set in men since their Fall. There is a bounder of every particular man arising from the proper corruption of his Parents. Beyond both these bounders it’s impossible to passe; yet happily one may arrive beyond the latter: nor yet so farre to go beyond it, as that the wisest of men can ever reach the former. Athough there be a possibility and aptitude of Nature to proceed to that boundary our first Parents set them. Let no man think this strange, since this aptitude extends itself to immortality, as appears both before the fall, and shall be evidenced after the Resurrection.
Perhaps you may object, That neither Aristotle, Plato, or Hippocrates, or Galen ever attained that prolongation. I shall answer, They have not attained the knowledge of many ordinary truths, which other ingenious heads have found out; and if so, they may easily miscarry in a business of such weighty consequence, though they made it their study: especially, if we consider, how they were burdened with other impertinences, and so were sooner brought to their gray haires, spending the inch of their Candles in more debased and vulgar subjects, than in finding out the wayes to so great Secrets.
[Frier Bacon His Discovery of the Miracles of Art, Nature, and Magick; Faithfully translated out of Dr. Dees own Copy, by T.M. and never before in English; London, 1659]