Thermal insulation between bathroom and the rest of the house is very relevant.
Bathroom is a room which is expected to be sometimes used naked, contrary to the rest of the house. Which means that the temperature in bathroom is expected to be kept at a higher value than the rest of the house.
For example, Polish building code in requirements for heating systems: in "rooms meant for constant occupancy of humans without wearing overcoats" (eg: a living room) - "ability to maintain temperature at least +20°C", while in "rooms meant for undressing or for occupancy of naked humans" (eg: locker rooms or bathrooms) it's up to +24°C. That's 4°C warmer than the rest of the house. Note that the law doesn't tell you to actually keep it that warm, just that you could if you wish so.
This example is not about requirements in a particular country, but about general expectations for a bathroom to "be able to be warmer than the rest of the house".
So, it's only reasonable to insulate a bathroom against the rest of the house, to avoid heating up adjoining rooms. Also, the bathroom heats up (eg from a long, hot shower) even if you don't meant it too. Having cold spots on walls would increase condensation there, leading to increased water damage.
Rockwool is not a sound insulation per se, but the empty space between drywall acts like a resonator - so filling it up with anything yields noticeable improvement. Filling it up with sand or concrete would insulate sounds even better, but the thermal performance would suffer. And would require tougher structure to cope with the extra weight.