And the people who are good at fighting games would not call them button mashers.
Yes, there are fighting games where you need to learn and execute ridiculous chord combos for certain moves. There are also some where you don't have that, there's a card-game version of a fighting game where people who don't have the finger-dexterity can play, and there's one fighting game with only a single button for each player -- and still considered a really good fighting game.
A good fighting game is rock-paper-scissors-break at it's core, with the whole idea that if you wait until you see the graphics of what the other player is doing, it's too late to block, but you may (depending on the game) be able to plan your next move. (Or not -- some games let your opponent juggle you once they get a hit.)
My biggest issue with fighting games is simply that I have yet to see one that is actually documented. Every one I've seen relies on each character having special moves that you have to experiment to learn, and no way to just go into "experiment mode" to practice, to learn them.
Experiment mode costs two quarters, and you can only do it when the Arcade is dead. Basically, launch double player, and whale on the immobile second player until you learn all the moves.
Of course, by doing so, you've now spent two quarters rather than one.