I don't think it's fair to classify GSP as purely a "karate fighter". Yes he studied Karate but he also studided Boxing at the same time. In later life he studied MT, BJJ, Wrestling etc... Interestingly he still keeps up his boxing training (he has a specific boxing coach) but he doesn't seem to have a karate coach that he uses in his MMA training. Not to say Karate can't be used in MMA, but when Muay Thai offers a lot of the same skills as full contact Karate but doesn't spend any time on kata etc.... People might still see Muay Thai as a more straighforward art to learn.
As for Machida, isn't his karate background very much the bouncy bouncy "one hit one kill" Karate that you weren't happy about in the first place Ken?
"Let your food be your medicine, and your medicine be your food"