But Kyokushin still spends time teaching people kata etc that Muay Thai does not. Many full contact styles of karate do not allow punches to the head, Muay Thai does. Hence why Muay Thai is more popular in MMA gyms.

I can't comment on Machida, I have seen both him and his brother compete in JKA tournaments though. And certainly as aplant mentioned, I don't know enough about "old school karate" to comment on it.

Back to my original point, if you are interested in MMA why learn full contact karate when Muay Thai takes less time to learn and offers at the very least the same results in terms of combative ability?
"Let your food be your medicine, and your medicine be your food" Hippocrates.