There were several generalizations in that statement that align with my similar fears to the OP. Most firmware should minimize the charge cycling, most batteries should be stable at constant charge... most isn't great for something that I want to sit in the corner undisturbed for a decade just chugging along - I have a few old desktops I use whenever I need a stand alone server or to host something web-live for a while. They'll eventually have hardware failures, but I have a lot more confidence that when they fail it won't be dramatic or destructive - ditto with old laptops, the serviceability expectations are much higher than phones so I have yet to meet a laptop I can't pop open and just pull the battery out of to run on AC alone - in the case of a power failure the UPS can't cover I'd rather the machine just power off rather than needing to deal with the possibility of dramatic failure.

I think if you're considering re-harvesting old devices to use for hosting and get far enough down your list to get to phones then you've likely got enough constant maintenance costs in overseeing things that the additional worry of fire risk just isn't worth it.