A simple nokia from 10 years ago or so will run for a week on a charge. It's only modern phones with massive screens, GPS, etc that eat battery.
The only real argument against pagers is that it's another thing to carry around, but in that regard modern pagers are a lot better than dumb-cellphones so pagers still have the advantage (because lets face it, people are still going to want their smartphones).
(Well, that and "they are old, and old is lame", which is not really an argument. ;)