[Maédhros]

He wasn't unable. They just took their rings off before he had the chance to do it.

They? It was Celebrimbor who noticed that, and it was after that that he gave the rings away to Erenion and Galadriel.
And if Sauron was able to control the minds of the wearers, how is it that Celebrimbor reacted fast and took off the ring/rings? Perhaps it is a process that takes time.

It does beg the question of : was it the ring, or Saurons innate ability as a Maia that enabled his reimbodiment? Im not sure what canon has to say about that. IMO your right most def after the last Alliance. But IMO, the post Numenor destruction w/o the ring Sauron would have regained the same form as he was post Last Alliance with the ring. If that makes sense at all...

From Ósanwe-kenta

Here Pengolodh adds a long note on the use of hröar by the Valar. In brief he says that though in origin a "self-arraying", it may tend to approach the state of "incarnation", especially with the lesser members of that order (the Maiar). "It is said that the longer and the more the same hröa is used, the greater is the bond of habit, and the less do the 'self-arrayed' desire to leave it. As raiment may soon cease to be adornment, and becomes (as is said in the tongues of both Elves and Men) a 'habit', a customary garb. Or if among Elves and Men it be worn to mitigate heat or cold, it soon makes the clad body less able to endure these things when naked". Pengolodh also cites the opinion that if a "spirit" (that is, one of those not embodied by creation) uses a hröa for the furtherance of its personal purposes, or (still more) for the enjoyment of bodily faculties, it finds it increasingly difficult to operate without the hröa. The things that are most binding are those that in the Incarnate have to do with the life of the hröa itself, its sustenance and its propagation. Thus eating and drinking are binding, but not the delight in beauty of sound or form. Most binding is begetting or conceiving.
"We do not know the axani (laws, rules, as primarily proceeding from Eru) that were laid down upon the Valar with particular reference to their state, but it seems clear that there was no axan against these things. Nonetheless it appears to be an axan, or maybe necessary consequence, that if they are done, then the spirit must dwell in the body that it used, and be under the same necessities as the Incarnate. The only case that is known in the histories of the Eldar is that of Melian who became the spouse of King Elu-thingol. This certainly was not evil or against the will of Eru, and though it led to sorrow, both Elves and Men were enriched.
'The great Valar do not do these things: they beget not, neither do they eat and drink, save at the high asari, in token of their lordship and indwelling of Arda, and for the blessing of the sustenance of the Children. Melkor alone of the Great became at last bound to a bodily form; but that was because of the use that he made of this in his purpose to become Lord of the Incarnate, and of the great evils that he did in the visible body. Also he had dissipated his native powers in the control of his agents and servants, so that he became in the end, in himself and without their support, a weakened thing, consumed by hate and unable to restore himself from the state into which he had fallen. Even his visible form he could no longer master, so that its hideousness could not any longer be masked, and it showed forth the evil of his mind. So it was also with even some of his greatest servants, as in these later days we see: they became wedded to the forms of their evil deeds, and if these bodies were taken from them or destroyed, they were nullified, until they had rebuilt a semblance of their former habitations, with which they could continue the evil courses in which they had become fixed". (Pengolodh here evidently refers to Sauron in particular, from whose arising he fled at last from Middle-earth. But the first destruction of the bodily form of Sauron was recorded in the histories of the Elder Days, in the Lay of Leithian.)

We have no knowledge (at least as far as I know) as to how many times a maiar who has become incarnate can "reclothe" himself when his hröa is destroyed. We know that the balrogs once their hröa was destroyed they didn't reincarnate themselves again. Although there is the mention of the orc-captains. It is my personal opinion that when Sauron's hröa was destroyed in the Elendil/Erenion fight, that he could not have survived without the One Ring. To me it was an anchor that allowed him to reclothe himself in time.

From Morgoth's Ring: Myths Transformed

This last point was not well understood in the Elder Days. For Morgoth had many servants, the oldest and most potent of whom were immortal, belonging indeed in their beginning to the Maiar; and these evil spirits like their Master could take on visible forms. Those whose business it was to direct the Orcs often took Orkish shapes, though they were greater and more terrible. Thus it was that the histories speak of Great Orcs or Orc-captains who were not slain, and who reappeared in battle through years far longer than the span of the lives of Men.

The footnote at this point, staring that 'Boldog, for instance, is a name that occurs many times in the tales of the War', and was perhaps not a personal name, is curious. Boldog appears several times in the Lay of Leithian as the name of the Orc-captain who led a raid into Doriath (references in the Index to The Lays of Beleriand); he reappears in the Quenta (IV.113), but is not mentioned thereafter. I do not know of any other reference to an Orc named Boldog,