Regarding legality:
Once in a fit of boredom I read through the entirety of the California Vehicle Code regarding this very issue. (I have sleep issues!)
In short, nowhere does it say you must have doors. Also, nowhere does it say you can remove them.
As I recall, it states you must not modify the car's body and must keep all permanently attached body parts. I presume that's to keep people from cutting off the roof, etc. However, since we're talking about doors, and as you point out, other vehicles come from the factory thusly, you're in in a decidedly grey area.
In the end the cop can ticket you for having an unsafe vehicle, with the unsafe-ness determined by the cop, not you. My experience, including driving without doors, is that if you drive politely and don't attract the attention of the cops, they won't go to the hassle of ticketing you. Make a lot of noise, drive too fast, or otherwise make a point of being seen, and they'll find a way to bust ya.
That said, IMO Burbs do look a little funny without doors, but that's aesthetics which are purely personal. Lots of guys here have mounted mirrors to the door hinges, or to the upper bolt that holds the quarter panel in. Be sure not to lose the shims underneath it though.
-- A