Breathe New Life Into Your Dead iPod
FreakyControl writes "Popular Science is running an article this month about how to change that dead iPod battery, along with links to sites that have other cool iPod hacks. It looks like Casey Neistat figured out how to do it for them, after ruining his own during a similar attempt: 'A few weeks later, PopSci gave him another third-party battery, this time from pdasmart.com ($60), and another iPod from a staffer with the same problem. That one survived and went back to its owner. And Casey ended up spending $400 on a new one.' Looks like all you iPod people may still have hope!"
As for the "sane" devices you mention: Looking at my Palm Tungsten T - there's no way to (easily) replace the battery in there, nor can the same be said about the other PDAs (Palm and Pocket PC) I see around me in my office.
Your rationale leaves something to be desired.