Hospitals use pagers because the frequency band they run on is better at penetrating walls. Shorter waves carry more data, but are easily blocked by walls. Pagers don’t need a lot of data, so they use really long waves.

And hospitals are built like bunkers, to avoid the potential need to evacuate patients during an emergency. Things like fire breaks between individual rooms, earthquake protections, being strong enough to stand up during a hurricane, etc… The goal is to be able to shelter in place instead of evacuating, because a mass evacuation of bedridden patients who all need monitoring equipment would be a logistical nightmare.

But this also means hospitals are really good at blocking wireless signals, because the walls are all super thick and sturdy. So they use pagers, which use long waves and can reliably penetrate the bunker-like walls. You don’t want a doctor to miss an emergency call because they were sitting in the basement; Hospitals need a wireless connection that reliably works every time. And pagers just happen to fit that specific niche.