In History's Strongest Disciple Kenichi, there is a scene that shows Odin, right before he meets Ogata Isshinsai, where he had just won a martial arts match that looks very similar to an MMA competition. He appears to make light of the competition and you do not see him use any common MMA skills in his later fights. Ryouzanpaku itself is set up to be for pure non-sport Masters. While there is nothing inherently wrong with this, the problem lies in the fact that it dismisses the combat effectiveness of MMA or its components just because they are used in sport.
Even Judo and Brazilian Jiu-jitsu are made to seem less than other martial arts. Ukita is a judoka, but always seems to be the weakest fighter in the group. And during the D of D tournament, the BJJ team got slaughtered by the Ancient Pancration team... Which should include wrestling as part of its skill set, but is never showcased. This is challenged slightly by the Command Sambo users, but it is an exception to the rule.
In Karate Shoukoushi Kohinata Minoru, Minoru learns Karate and a little BJJ and does very well and then Mutou just does Karate and is ridiculously more powerful; however, a fighter from the MMA club is taken down by a single front kick (mind you, from a very strong karateka, but all the same). In general, if someone does MMA in manga or anime, expect to see them get slaughtered.
There are exceptions to this in Grappler Baki, Tough, Teppu, All-Rounder Meguru, and some others, but in general, MMA catches a bad rap in anime and manga. There's nothing wrong with just Karate or just a style of kung fu or just boxing or whatever, but the problem is when an author belittles the fact that MMA has fundamentally changed martial arts for the better (another article) and that mixed martial artists defeat traditional martial artists on a regular basis. I've said this before and I'll say it again, if you want to be a pure karateka or boxer or wrestler or whatever you have got to push the limits of your fitness and strength and find ways to deal with your style's shortcomings. Don't blame your art. Pick your path and charge full speed ahead, but prepare for the trials and tribulations and don't expect to win just because you train hard. Scissors always beat paper, no matter how much you don't want it to.