Most of these devices can't run "without touching the battery" because the external supply can't provide the required peak current, so during some CPU burst it would shut off.
I've seen hacks that replace the battery with a supercapacitor though.
Couldn't the power management simply throttle the CPU to never go above supplied power in a battery-free mode? Don't they already implement a power threshold for degraded batteries? It seems like that would just be part of the feature I'm asking for, and easy to implement.
It really seems like, if it weren't for the battery part, these phones could run for decades... but right now you have to replace the battery every couple years because it swells when constantly kept at 100% which it is not designed for.
I've seen hacks that replace the battery with a supercapacitor though.