I don't think there's any real system in place that would make for a good platform for allowing any of those sports into the Olympics. When it comes to sports built around the martial arts-- literally around fighting, meaning you're risking getting a bad concussion-- and it's in the amateur spectrum of the sport (meaning you're not getting paid to compete, you're just doing it out of passion), there has to be a middleground between full-fledged competition and fundamental-based competition. That's the reason amateur boxing looks so much different from professional boxing, and why pro boxers wouldn't even be able to win Olympic-level amateur boxing matches [rules and scoring are so different], and why Olympic Taekwondo and Karate are different from kickboxing. The rules have to be built around different things since they're not competing as professional martial artists.
If you watch more amateur fights and submission grappling matches, there's a pretty quick realization: there is no middleground like that. No amateur MMA system actually provides a good baseline for preparing your skills and graduating to professional levels that would allow for something like acceptance into the Olympics. Amateur fights are basically just shorter pro fights that you don't get paid for. If it wasn't for the three-minute rounds, you wouldn't have thought there was anything different about Cody Garbrandt's amateur knockout loss from his professional knockout loss, and that's what most amateur matches fall under. Malaysian Invasion has a great amateur system, but you watch their fights and you just go, "So it's a full fight, they're just wearing shinguards?"
The closest thing to having the kind of idyllic system needed for the Olympics is Shooto with their D-class and C-class amateur matches, but nobody who thinks "MMA at the Olympics" actually thinks about something like D-class Shooto matches. They're thinking something like, "Holy shit, it would be cool to watch Conor Mcgregor knock somebody the fuck out at the Olympics and then stand on top of the Olympic cage and do a backflip!"
And submission grappling can't even come to a consensus about what the ruleset should be-- a lot of people hate IBJJF rules, and you can't have "matches are 15 minutes, it's a draw without a submission" rules in the Olympics. If the sport of submission grappling itself can't come to a consensus, how is it supposed to get accepted into the Olympics?
Combat wrestling is the only real form of submission grappling I've seen that could be viewed as an acceptable Olympic sport, but nobody wants combat wrestling in the Olympics...
