I can't answer the question from original documents, however, the trunnion of a Coehorn-style mortar would spread out the recoil force over a wider area, its inletting would be a relatively simple machine-performed process which would provide a better fit, it would prevent the tube from turning in the mount and it provides points of purchase to retain the tube in the mount. Maybe even more things I can't think of right now.
And maybe it was just tradition.