

Because as a headless server it’s likely to sit hidden for a long time. This and the always being plugged in is not good for lithium-ion batteries. If/when it starts ballooning will you notice? It’s a fire risk.
UPSes use typically lead-acid batteries like a car.
You can typically replace the battery inside the UPS (and should every few years). Looking at $40-50USD for “official” replacements, less for questionable third party ones.