It's at least partly to do with the increasing weight of the aircraft. A 200x60 tailwheel tyre was rated by the Germans as good for a 200Kg static load whereas a 290x110 tyre was rated for 450kg.
Sengfelder alludes to the later tyre types having a much longer service life but doesn't specifically apply this to tailwheels.
Most late war German fighters were supposed to have tailwheels that retracted (at least partially). Unfortunately the retraction systems,particularly on Messerschmitt fighters,were not always reliable.
Steve