People do eat all parts of the alligator and make dishes like gator nuggets and alligator legs.
I've just seen in a show also that making a dish of a gator meat, but I haven't tasted it yet and I think, I won't dare to try to eat it. 

Only time I've ever tasted Gator was at a fun little rustic drinking-joint just outside of Fairbanks called "Two Rivers Tavern". It was simply cut into strips- battered and deep-fried and I forget was sauce it was served with. If I hadn't known I'd have thought it was chicken strips. Parts is parts- HA! 

