And there doesn't seem to be a way to get only email and not DW inbox.

Ah, yeah. That's part of the code they inherited from LJ -- if you have a look, you'll see that the LJ inbox actually does the same thing (it used not to, but now it does).

(There's some complicated technical reason for this which vanished from my brain the moment Syne finished explaining it to me.)

I find it annoying too, but the inbox does automatically start deleting messages once they hit a certain number. I just go and "Delete All" occasionally because it makes me feel better.