Have you tried "Quo Vadis?" by Reiner Knizia? It's very simple and elegant and strips out everything but the politics. It's probably the game that convinced me that not all political games have to be bad.
For me there's several big problems with political games:
1. Players have to choose between building up their meta and probably winning more games with the same crowd in the future, versus winning this game now. What I mean by that is, I tell you I'm going to do something, and now it's advantageous for me not to do it, do I hold to my promise anyway because maybe players will trust me more in future games I play with them, or do I break my promise so I can win this game. I hate this because it brings outside considerations into the game, like "am I likely to play more political games with this group".
Quo Vadis? solves this with binding promises. If you say you're going to do something, you have to do it, so there's no meta to worry about.
2. Players always choose to go after the current winner. Maybe some people find this fun, trying to slog their way to victory while everyone's going after them, but I don't know, it just seems really frustrating, and in a lot of cases (like Settlers of Catan or Risk) it means players are just voting on a winner, and if we wanted to play vote on a winner, man why did we spend hours moving pieces on a board. Also in many cases it means the game never ends with optimal play, I feel like I've played games of Risk where power just rotates and it's always player A vs. everyone, then player B vs. everyone, etc., and there's never a point at which it's optimal to rebel and go into free-for-all mode because that just mean whoever is in power now wins.
I think Quo Vadis? attempts to solve this with hidden VP, which is nice I guess but I don't really like it because in reality it just rewards players with a good memory. It may still have the "vote for a winner" problem occasionally, I haven't played it enough to know if that's an issue, but I like that it at least attempts to solve it.
I don't think political games have to be bad, but I think most of the ones that exist are bad either because of one of the problems above, or because they weren't meant to be political, and the politics are just a consequence of badly designed mechanics. And given that Quo Vadis? exists I don't think I'll ever play another political game and think that it doesn't just boil down to Quo Vadis? with lots of bells and whistles.