Added the video to bolster your statement. This has been answered throughout the last 20 years of the sport which probably Old Fan and myself have seen LIVE from the start.
The karate that is learned is not very applicable to MMA prior to the nascent of MMA because it's for self defense as is most traditional arts classes. Everyone else uses some aspects (spinning side kick, some stance, punching techniques), but once you're fighting another striker the dynamic of the fight changes because you have to use different kinds of movement. Then once you're facing a grappler the dynamic changes again.
As Old Fan mentioned Machida is learning from a Shotokan master. They've tailored it to an MMA setting. He's one of the few that uses the traditional stance and fight system in it's totality.
I don't think people shit on it for the sake of it at least not any more. Many in the UFC are karate practitioners including GSP. Some do Tae Kwon Do, Jeet Kune Do, wu shu (Roy Nelson) shaolin (Dan Hardy), Capoeria, and many more.
The answer to this was done 20 years ago. Every decade the game evolves. We've now come to the point where each champion is proficient with at least two to three different kinds martial arts.
Unfortunately the newer athletes will be jumping straight into the hybrid mma classes where some of the traditional values will be lost.
Look at Lyoto Machida vs Shogun I and II. Muay Thai generally speaking is the most effective in an MMA setting and in the streets. You need to take muay thai classes to understand the difference. Karate, Tae kwon objective is to essentially disarm an opponent using point systems. Muay thai is aimed to BREAK YOU hence why there's elbows, knees, and kicks where you use your entire hip to swivel and chop your opponent.
Anyways take it for what it is. My advice go to a local MMA gym and challenge/spar with a muay thai intermediate student and see for yourself how effective karate is.
Marcus Aurelius: Tell me again, Maximus, why are we here?
Maximus: For the glory of the Empire, sire.
Baked, not fried... the healthy choice.