Generally, as long as you keep the phone plugged in, the battery should be safe virtually indefinitely - the battery management on board will keep it in a state where its a constant charge which means the chemistry will be stable.
Would you say this is a chemistry/QA problem? Have there been advances in battery / controller technology that achieves the above?
(My current machine is a Thinkpad P52 if it matters, but I also use older Macbooks and newer Thinkpads and older Dell machines this way, although they're plugged in less often these days.)
2. Open up the laptop and check if battery is swollen. After about 10 years, it's also a good idea to replace the CMOS battery before leaking.
3. Without opening, sometimes keys/trackpads don't work anymore as expected. This might be due to swollen battery packs (we had several Dells where this happened).
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.
Batteries, however, are absolute hellfire when they go wrong (because of chemistry - not just the temperature).
What is your source on this?
I've replaced the battery in always-plugged-in iPhone 3 times over 10 years because it was expanding into a spicy pillow.
I too want a way to run phones directly off of USB power, without a battery present.
Never again. I was genuinely shocked the thing turned on once I closed it up. It's one thing to have a conceptual understanding of how tiny the components inside a phone are. It's another thing to actually be trying to seat a plug into a socket with tweezers and just have no idea how you're supposed to tell if it's fully inserted or not.
Could have been worse -- the sentence could have ended right there...
(This is for a removable battery, but should be close for built-in ones too, I suppose)
[1] https://www.youtube.com/watch?v=7f8SliNGeDM&pp=ygUYZ3JlYXRzY...