I agree, renting a girl friend seems not quite convenient concept, but I think the characters and events are entertaining. Maybe that because I like these kind of relationship stories.
Main character is really annoying, but while I was watching, I never tought like I have never seen this kind of guy.
Side characters are maybe one of the best aspects of the story. Mizuhara, Sumi, Ruka, the fighting guy... All has their own evident personality. In most animes, you do not understand the personality of a character for 200 episodes. Does any of you know what kind of person Asuna is? You understand motivation of all characters in 12 episodes in Kanojo Okarishimasu.
Jealous girlfriend is an amazing villian concept. Aizen, Itachi, Doflamingo, what ever... Mami-chan is much more than these guys. Anime history have not seen any villian character like that.