I know I'm biased because I'm a HUGE Tim Drake fan, but I think he belongs on the Teen Titans. The Teen Titans should be made up of the biggest and best teen heroes of today, and Tim certainly fills that criteria. Also, the team is made up of his best friends. It makes sense that he'd be a part of that.
I feel it's wrong to have characters like Superboy, Wonder Girl, and Kid Flash on the team and then say it'd be boring or predictable to have Tim on the team. Why should he be the only one who is excluded? The Titans need a member of the Bat-family on the team to be whole IMO, and Damian just isn't a good fit. I would love it if Stephanie joined the team, but I'd still want Tim there too. Honestly, to me, it's even more specific than just any Bat family member, a Titans team isn't complete to me without either Dick or Tim on a team (which one depends on the age group of the Titan team).
Personally, I think Tim has been criminally underused since he became Red Robin. The only book he has steadily appeared in is his own. Sure, he's had some occasional guest appearances, but nothing permanent. His appearances in Detective Comics and Batman are not regular. If he became a full time member of the Teen Titans that would make him a regular in two books. That's not overkill. I mean, Conner is a regular in two books. Hell, Dick is in Batman, Detective Comics, JLA, and Batman & Robin plus guest appearances in other books.
Honestly, I don't think if Cassie stepped down as leader it would reinforce the "no one knows how to write her anymore" thing. She doesn't have to be leader to be written well. I think if she stepped down they could focus on getting her back on track and try to forget the crap that's been going on these past couple of years. It wouldn't have to be a demotion or anything. She could just realize that Tim is the right person for the job. I just don't see her leading a team with Tim on it. That dynamic just doesn't make sense to me. Yes, again, I am biased, but given the way the team dynamics have been written in the past it would seem odd to have Cassie lead Tim. And really, Cassie only assumed leadership because Tim left. She didn't show any real desire to be the leader, but did so out of necessity.