From what I understand the big American aircraft companies did not like the wood and glue building materials. They felt it was below standards. This included Beech aircraft who made wooden planes. You are correct though that the 8th Air Force had no problem operating the Mosquito.
That was what I was going to post. The USN operating mostly in the Pacific wasn't confident how well a wooden composite airframe would stand up in a hot and humid climate. Despite the excellence of the DH Sea Hornet and Hornet that was a valid concern. Even a modest airplane like the Fairchild PT-19 trainer developed problems with its wooden wings operating in the Southern U.S.
I think eventually de Havilland developed better glues to withstand the tropics humidity. But post-war the Americans were going to jet aircraft anyway.