The biggest drawback to the high rate of fire was that the barrels would heat up very quickly, but the engineers thought of that. The MG81 (and the MG42 shown next to it) had incredibly simple and fast methods for changing barrels; the standard kit included a second barrel as well as an asbestos lined mitt.
There's a scene in Saving Private Ryan where they're attacking an MG42 emplacement and Tom Hanks' character instructs his men to not make the final rush against the position until the MG crew has to change their barrel. This leads me to guess that standard practice was to rotate barrels after maybe 150 rds of continous fire (since I'm guessing that's about 3 belts of 50 each).
Granted, my knowledge comes from reading books and watching documentaries.