I always toss my shirts in the dryer, with the exception of the ones that go to the cleaners for laundering and pressing -- and I'm pretty sure they tumble-dry them as well. They're shirts, for chrissakes. Life's short. If they wear out buy new ones.
And maybe I'm lucky but I don't think I've ever retired a quality shirt due to wear. That includes MTM shirts that have been worn in regular rotation for 6 years.