What evidence is for this really? Wouldn't it be more accurate to say they didn't create, and continue not to because it would require them to sacrifice bits of themselves?

The Aedra gave up their power, if not lives and divnity, to create Mundus. Technically, the Daedra could create and do so metaphorically with their realms, but for them to instantaniously bring forth life and creation, it's going to cost them.

They did not help Create mundus, that's for sure. I imagine that they're now permanently separated from ever participating in such an act; or they can but lose power immediately. Can't really say.

The daedra definitely corrupt and change things though --- dunmer, malacath, vampires. Curses, blessings, etc. Even the daedric realms and artifacts are just manifestations of a Prince's power

Not offering any evidence for or against, but not expecting any firm evidence really. I think it's probably a traditional Cyrodiilic dogma. In all truth the Aedra have never really "created" since the beginning time. And it seems rather arbitrary to say that those bits of Oblivion that intrude upon our realm (Daedric artifacts, lesser Daedra, bound weapons) are not "true" creations.

I just don't see any cosmic rule preventing them from doing so if they pleased. There is no real difference between Daedra and Aedra aside from participation in the creation of Mundus. They are both Et'Ada with classifications given to them by mortals.

It's not that they can't, it's that they won't.

As Daedra, they cannot create. If they participated in creation, they would no longer be Daedra.

Creation, for the Aedra, means cutting off a piece of yourself and allowing it to grow independently. Daedric realms and their servants are projections of themselves, and dependent on the creator. If Mehrunes Dagon were to blink out of existence, the Deadlands and its occupants would follow. If the same thing happened to Stendarr, Tamriel would endure.

They can't, because by their nature they never would. Just look at how Clavicus Vile reacts to Umbra's assertions that it is a separate entity.

I think, when the books say that the Daedra can't create, they mean more specifically that the Daedra can't create on Mundus, because they have no connection to it. They can create plenty in their own realms, which are parts of themselves. There's nothing I can see that says that Daedra can't go and create their own version of Mundus whenever they please, but the fact that the Aedra suffered in order to create the Mundus we're familiar with is probably a serious disencouragement. Moreover, why try to create mortal life to play with when those other fools have already done it for you? No reason to suffer when you can play with someone else's toys at no cost to yourself.

Creation is fundamentally more opposed to Aedric nature than Daedric, or so I see it. When Mundus is created the Aedra that pour themselves into it necessarily die. I like to think that this is due to them negating their Anuic nature of stasis. The only surviving Aedra that aren't in Aetherius are those that play more of a "changing" role in creation than a "making" one. They tend to pull things in the direction which is natural for them (and for Akatosh as time, creation is the perfect place to assert his nature). Hence we have Kyne and Arkay and Julianos and the rest of them who are surviving in the changing cosmos by asserting part of their identity, and thus not negating it. In essence, they are repeatedly chiming their familiar myth-tune that happens to be still in tune with Mundus.

As for the Daedra, if we view them as strongly "Padomaic" (I don't think they are), then it's altogether possible that they just can't survive in a world that combines both stasis and change. Few of the Daedra are really as "strong" as the Aedra in a mythic sense, even if the Divines are distant and harder to interface with than Oblivion, and I think this is because the Aedra get strength from their contradictory nature. If the Princes of Misrule were ringing out their own tunes (which are much more clearly defined than those of the relativistic and even contradictory Aedra) then the resulting discord could well destroy them permanently, but weave part of their nature into Nirn in the process. As it is, they've got their own little realms of change which can survive the winds of the Arena below.