I do actually have a Jamstik Studio guitar which has a USB-powered rechargeable battery, but that also has a MIDI converter in it which takes a fair bit of power.
I've also got some Variaxes (Variaces?) which also have large current drains and use two different types of battery. The older ones use a 9V supply (generally in the form of 6xAA batteries), while the JTV ones have a slide-in battery like a smaller version of the battery pack powering cordless power tools. The latter is more convenient, and would be more convenient still if you just plugged a USB lead into the battery pack.
One day, all basses will have an on-board computer. Except Fenders, obviously.