I think it's because you're only meant to plug shavers there, which are designed to work in humid environments.

Other equipments should not be plugged into those sockets, so the physical design prevents it.

It has less to do with humid environments and more to do with grounding in general. You can find 3-pin outlets in most bathrooms in Europe, they're typically used for hair dryers and washing machines.

If equipment is designed with sufficient insulation that prevents users from coming in contact with the mains voltage in cause of malfunction, 2 pins are generally enough. Otherwise any electrically conductive parts need to have a connection to ground through the 3rd pin to prevent risk of electric shock.

I would think it's because of the different current specifications.

In the UK most electrical outlets are on ring circuits that are limited to 32A - that's a whopping 7.5kW. Fuses in the plugs of specific appliances provide additional protection with 13A being the largest (3kW) required.

Bathroom outlets are required to have a separate transformer that isolates ground. This prevents the possibility of any electric shock from a short to earth. The current the isolated transformer provides is limited so connecting a regular appliance cannot be allowed.