In theory they'd be more consistent across the platform, just like text and select boxes; I'm not seeing the problem. You're site doesn't need to have it's style imposed on every single control.
> 2. What the UI looks like is still in flux and will likely remain in flux. This means that not only do you have to test/support all the currently provided UI, but you also have to be ready for unexpected changes in the future.
Why do you care what the UI looks like? As long as the API is stable.
> 3. Specifically because you cannot change what the (fairly complex) UI looks like, you cannot make it match your theme. This can be a huge pain.
I count this as a plus, honestly.
> 4. There are better JS-based datepickers out there for the desktop.
Ugh. The less we rely on javascript for basic functionality the better.
You're js, highly themed date picker probably isn't very accessible and probably doesn't function like the rest of the system does either.
The more we can leverage the User Agent, the more we should. It's easier on developers. It's more accessible. It's more consistent across the user's platform.