I have no problems with finger vibrato, with a vintage style trem bridge set to float. It does drop the pitch of other strings when you bend one. You can compensate for it a bit, but of course it's a compromise..as is also a trem bridge that has been setup for dive-only action. With that, you'll lose the bar vibrato. I've tried both. You'll probably lose some tuning stability (with trem use), if you set a vintage style bridge flush to the body.
I believe Steve Vai uses or at least HAS used a device like tremsetter. With that, the guitar doesn't drop pitch while bending strings (I don't know HOW far you can bend before it releases), but naturally, it'll change the feel of the trem. A natural sounding bar vibrato is probably a bit trickier, I haven't tried one to be honest.
And when playing with a fixed bridge equipped guitar, I don't have to worry about those kinds of things. Not the good or the bad :D It's all about choosing the most appealing compromise. And owning different kinds of guitars 8)
-Zaned