FormerlyHemlock
Hero
Well the mechanics around renown aren't as specific or as granular as yours (understandably so since they are designed more for the DM to use as a baseline and tweak for his particular vision) but they include rank... attitudes of organization members, perks, and rules for increasing renown during downtime. I mean I understand if you're not keen on the particulars but it is pretty adaptable and, at least IMO, very similar at a more high/generic level to the rules you've posted. All that said... I don't think it's correct to claim 5e doesn't have a system like this when it fact it does, even if said system isn't granular or specific enough for your tastes. It's like claiming because 5e doesn't have a way to allocate individual skill points... it doesn't have a skill system.
I believe I said that 5E doesn't have a game structure for politicking, in the sense talked about here (http://thealexandrian.net/wordpress.../game-structures-part-2-game-structure-basics, http://thealexandrian.net/wordpress/15140/roleplaying-games/game-structures-part-3-dungeoncrawl). I don't think the DMG rules count as a game structure. I could be wrong about that.