Pagers, in their niche, are better than any other technology available. Considering how often my phone battery runs dead by accident, I feel a lot more comfortable with surgeons having pagers that run for months off a single AAA battery.
A week is a far cry from months. Range, reliability, and delivery guarantees are also an issue with phones.
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. ;)
I'd like to know where you're finding a pager that runs for months on a single AAA. My pager takes a AA battery, and it has to be replaced roughly monthly. Why, yes, I do work in Healthcare IS, why do you ask?