Haha yes, but it doesn’t last for more than 20-30mins now. Used to be 7-8hours for the first five-six years, then dropped off.
I also only buy used phones (I don’t have high requirements) and as with laptops, batteries are the “weak link” - as you correctly point out.
A brand new battery for my laptop, can be had for ~30-65 USD though, and the battery is easy to replace (doesn’t even require screwdriver). I never use it untethered anymore though, so I don’t bother..
For me they usually just lose capacity and/or ability to charge. Most laptops will keep functioning when tethered.
I think most batteries must puncture or corrode to pose a physical hazard. Alkaline batteries can corrode, but I’ve never seen issues with old Li-Ion unless exposed to violence and/or water.