The pagers carried by doctors are usually specially designed to provide local coverage. A mast is installed at the hospital, and it provides guaranteed coverage of the whole site. E.g. in the basement, in the lead lined rooms of the X-ray department, etc. This is particuarly important, for on-site doctors who may need to be respond very urgently.
Additionally, the on-site systems are usually specially customised for the site requirements. E.g. For extremely urgent calls (e.g. cardiac arrest, a voice message can be broadcast to selected pagers. So there is no need to read the display, or get to a phone. The message can be acted on immediately).
Cellphone coverage can certainly not be relied on in very large buildings (especially, in basement or underground areas).
Some doctors who need to be contactable while off site, may carry a pager that uses a commercial network as well as their on-site pager. However, in many areas, off-site cellphone coverage is sufficiently good that many doctors simply use a cell phone if they are on-call but not on-site. (Usually what happens is they'll leave a series of contact numbers with the hospital switchboard operator, who will forward calls).
Commercial pagers also have the advantage that they don't require as strong or clear a signal as a phone - so their range and coverage is better.