Random? Random?! Nonsense! Just because a fighter requires lotsa buttons to be pressed doesn't make it "random." Sure, sometimes you can just mash buttons out and you'll get a combo. But that's like saying you can throw a box of chicken broth, a jar of peanut butter and a cheeseburger into a pot and get soup.
Fighting games get a bad wrap from most gamers. The issue doesn't lie in how they're impossible for a new player to pick up, it's just that they're they require precision, which is something that's tedious, boring and time-consuming to acquire. The fighting games that do allow for easy execution and have the "pick up and play" element just plain suck.
Soul Calibur, for example, once you distill everything to the one best strategy, becomes nothing more but a poke fest. And not in a good way. If you pull up a tourney vid of Soul Calibur, all you see is Xianghua doing her crouching A or her uppercut B. Repeatedly. Soul Calibur boils down to two of five characters doing the same two moves again and again and again hoping that one hits, and that they hit enough to kill the opponent. Are there elaborate combos and juggles and massive command throws? Yup. But does any of it matter? No. Like so:
http://youtube.com/watch?v=p_WXb8cVs68
Watch the Sophitia. Note what they do.
King of Fighters really doesn't have all that much to it in terms of crazy abilities that everyone has. There's short jumping, rolling and one or two more, varying between games (be it cancelling, guard breaking, just defending, alpha countering, etc). The 99-2k1 era brought the assists and the 2003/XI/XII era brings in tag matching. But that really just adds diversity and the whole cool-looking stuff to the game (while adding another dimension to some characters).
Guilty Gear is really the game that brought out a lot of stuff. The thing is, Guilty Gear is way, way, way out there as the most-balanced fighting game, ever. In tournies, literally every GG player is used, compare to Street Fighters where between three and five are used out of a cast of 20+. GG really does have a whole, whole lot. Every character fights entirely differently from other cast members, it has modified gravity, damage scaling, alpha countering, roman cancelling, green blocking, bursting, a far-more-complex guard meter, and all sorts of other stuff. While it might scare away most players, in all likelhood, they'd be scared off when they learn that you can't just make things up as you go along in Street Fighter 2.
Killer Instinct was something similar to Soul Calibur, but it ended up getting broken into pieces by the silliness that is the combo breaker. Because of it, everything boiled down to one move. Seriously, a KI match where both players actually know how to play the game is one of the ugliest PsOS you'll see. Like So:
http://youtube.com/watch?v=sC-sofTQ3ZI