Getting 'locked' into a physical form for the Ainur seems to have a combination of causes.
Melkor can appear fair (in the beginning), but after he takes the evil warlord in Utumno guise on, he....gets stuck. He loses his ability to shift into a fair form again, or into any different form. This doesn't happen until the destruction of the Trees and the theft of the Silmarils (if I recall correctly), so until that time, he can go from monstrous to fair at will. The monstrous form wasn't *necessarily* a consequence of his fall (he chose it willingly, at the time), but the loss of choice is definitely a consequence. His face really did get stuck that way! (On a related note, that's why his scars stay with him as well - the silmarils burned his hand, Fingolfin made him walk with a limp, and Gwaihir clawed his face...he can't undo any of this.)
Sauron has particular skills as a shapeshifter, as his stint as a werewolf reveals, and he can maintain his fair form (when desired) all the way until the destruction of Numenor. In both those stories, it is brought up that his power is greatly diminished if his physical form is destroyed/killed - if he has to flee as an unclad spirit, it will take him a long time to rebuild himself. That's why he chooses not to escape Huan, and instead yields the fortress. And the drowning of Numenor would have been the end of him, but for that magic Ring......
Both Gandalf and Saruman are slain in Lord of the Rings. True, Gandalf's battle with the balrog is hardly recounted in a way that makes it clear what really happened. But it sounds very much as if his spirit left his body abandoned on the mountainside for a time, and after healing, he was sent back to it (himself?) Saruman's spirit dissipating in the wind isn't unlike the death of Sauron. But the Istari seem to have been locked into the forms of old men for their mission to Middle Earth.
Melian, in choosing to marry Thingol and give birth to Luthien, locks herself into that form as well. It's not just a fall that takes away the choice...it can come of investing strongly in the physical realm of Arda, so.....
In the case of protobalrogs (angels) --> balrogs (demons), I'm not sure what would be best. Showing the transformation as a natural consequence of their choices is important (rather than an external punishment afterwards). But whether they willingly assume these forms for stealth/destructive power in preparation for taking out the Lamps or they get caught up in the destruction and burned/marred perhaps depends on personal preference. Or perhaps a combination, where we seem them burning from the inside out, and then caught in an avalanche of molten fire.