Repairing Damaged Drywall Around a Bathroom?
To my mind the solution isn't dependent on your choice of joint compound (though topping compounds lack the vinyl component which can help with bonding). Even if you use concrete to coat it, what's behind it is still susceptible to water damage. Instead, moisture management and a good primer/paint coating is important. Your walls simply shouldn't be exposed to prolonged moisture. 

I'd scrape away all loose material and finish the surface with whatever mud suits your fancy. Prime it with something that seals well, and use a high-quality topcoat that claims to bond well and protect against moisture damage. 

An exhaust fan should be on a modern digital timer. Run it for at least two hours after a shower, as the moisture stuck to the tub and your towels takes a while to evaporate.