I know some aikidoka (many times my seniors) who wear their gi to class. Not to mention they treat their hakamas and uniforms in unthinkable ways.
I guess they either find it practical or believe is historically acceptable. But I ask; is such a small convenience worth all the attention and possible trouble you attract?
I think that the "attention and possible trouble" issue is way overblown. It's a matter of common sense, I suppose - if you're walking across Times Square it may be an issue, if it's a 5 minute drive in a small town than it probably isn't.
Besides, weapons bags are probably more attention getting than a dogi anyway - just try carting around a naginata or a spear :-).
I'm not sure what you mean by "unthinkable". I think that, on average, Japanese people tend to be more finicky about care of dogi and hakama then westerners, but that has nothing to do with budo and everything to do with the fact that Japanese are pretty finicky in general.