>>The problem with modern smartphones is that they run on battery, even when plugged into external power.
That's not universally true - a lot of android phones have a "bypass charging" mode where you run directly from the power supply, and indeed you can run them with the battery removed.
I think sometimes playing games on the phone while plugged in would actually drain battery because the CPU just used too much power (obviously a while back when charging was lower power).
Not sure if those phones would work without a battery and throttle the CPU, or if they would crash.