The Flat Duo Jets are one of my top favorites too - they fucking kill it as a two-peice, but their first album with Tone on upright bass was a real gem also. The Cramps went for years with out a bassist too, no? I don't think anyone could say their music suffered for it.
I see where the OP is coming from, but some bands can certainly pull it off to great effect. One man bands? Rhythm is usually as simple as a stomping foot or thumb taps on the body of their geetar, and it often suits their music well. I highly recommend Scott H. Biram for a great showcase of what one person can accomplish on their own.