Really, I've never been humbled by an axe kick or a spinning back kick. The first gives me a nice single-leg slam, the second a suplex.
Oh I don't know about that I fought a tkd fighter and was humbled by his front kick and spinning back kick, not to mention his axe kick. plus is snap kicks are very hard to defend against because if he has speed you don't know where there gonna end up. geoge st. pierre and jason macdonald use tkd in their fights.
The snap kicks don't do as much damage and are just as easy to catch as any sort of thai kick.
GSP is actually a karate guy (as is Loiseau, who you didn't mention, but very well could have). I'm not sure about MacDonald's background.
Then again, Danny Abbadi is a TKD guy, so what representation they do have in the sport in terms of purists is, well, bad.