Funny enough, I remember back in the late 90s and early 2000s that Tenchi was called the anime equivalent of a door mat. It was mostly in jest, but at least Tenchi bothered to have a backbone in most of the continuities. With Tenchi in Tokyo giving him the most backbone, ironic enough. I don't know much about the show you watched, but from the premise I just read, it sounds like the 1980s version of Love Hina, but better. Don't know much about the character, Godai either, yet I feel Keitaro is a much bigger door mat than the former.