Jesus didn't have to; his audience was already steeped in Leviticus 18, and one of the ways they saw themselves as separate from the Gentiles was in their unwillingness to accept homosexual acts. Paul, OTOH, as the presenter of the gospel to those same Gentiles, would have to have confronted the issue directly, which he does, to the two groups whose local cultures would have been most steeped in homosexuality: Rome and Corinth.
Very good! I had thought aboutthe first part but not the second part.