Battery Powered Preamps

I notice that the more expensive preamps get within a line, or in general, the more complexity and expense seems ot be applied to the power supply and regualtion; sometimes with the addition of a second box for the power supply.

I conclude power supply is important. If this is so, why not go the simpler route of battery power for pure DC? My Dodd Battery Pre works very well indeed (for context -I've owned CAT, Lamm, ARC, Joule, Placette Active, Atma-sphere (still own), Bent TAP). Am I missing something, or doesn't battery power just make the most sense for a preamp - off the grid and all that? Seem much simpler than most highend approaches, and much less expensive to implement.