The barrel change is based more on heat then wear in the field. If it gets too hot the dispersion opens up beyond acceptable limits, and there is also the risk of the ammo cooking off in the chamber potentially leading to a runaway gun. Water cooled guns from WW1 could, and frequently were, fired for LONG (several hours) periods of time. Basically so long as the water and the ammo held out they would be fired pretty much indefinitely.
There are both rate of fire (RoF) and time of fire recommendations on when to change a barrel. For instance rapid fire might be a burst of 6-10 rounds (RoF) every 10-15 seconds. After 3 minutes of rapid fire the Field Manual (FM) might call for a barrel change. Full cyclic (holding the trigger down) might call for a barrel change after 1 minute. Different guns, different ammo, etc all dictate when a barrel change should be made.
As CapnMac discussed, the Wehrmacht was different the US Army in that they felt the MG was the primary killing arm. Their MG's tended to have a much lower dispersion then American MG's, and a much higher RoF. The goal was to place a killing burst on a given target, even if it was rapidly moving or fleetingly appearing between cover. American MG's had a much higher dispersion and much lower RoF, they were designed to fix and pin an enemy. Against enemies in the open they were just as deadly as anyone else's MG's, but against a single rapidly moving point target they weren't as effective in killing/wounding. They could however put fire down on a larger easier much more efficiently, and for a far longer period of time with a given supply of ammunition compare to the MG34/MG42.
The MG42 would heat up faster due to the higher rate of fire then say the M1919 MG when firing a given quantity of ammunition, and it would be capable of firing it far faster than the M1919 (approximately double the cyclic rate). This would lead to a loss of acceptable accuracy, as such it would require more frequent barrel changes then the M1919, but this was offset by the ease (comparatively) with which it was done on the MG42.
The MG42 spare barrel case was actually designed to help cool the hot barrel while it was out of rotation. The barrels were not cleaned until after an engagement was over typically. There was no real reason to clean the barrel before putting it back into action.
-Jenrick