I always though NUC's are designed to be cheap, quiet, and small, not power efficient. I don't think they run on battery power.
I ran one on battery power, IIRC some models run on voltages in the 12V-20V range, so it is pretty easy. Fun project. I got a portable monitor and keyboard, and… realized I’d reinvented the laptop, except it was really hard to balance all that stuff on my lap. Next time I just got a laptop, but I can still use all the old NUC peripherals so that is nice.
It's easier to make something small and quiet if it's power efficient. It will need to dissipate less heat.