Fighting games are a complete genre, yes, but not all of them follow the rules you're complaining about. Smash Bros. has already been named in this thread. There's a massive number of games with rules similar to fighting games, but that have changes that alter the fundamentals.
As you denoted, the lesser versions of Fighting games with simplified combos and special attacks are dull. They don't really change how the game operates, they just make attacking pretty colorless and repetitive for most experienced gamers who aren't too familiar with traditional fighters. That's probably similar to how the guys that go on the driving range and would love to play nine or eighteen holes any given day feel about mini-golf, too. And c'mon. HORSE is just a lame game, and we both know it.
Dumbing down the rules can create something anyone can play, but it's only fun when the game was designed for simplicity from the ground-up. HORSE is entertaining for a little while, but once you really get the hang of the real thing, if you're a basketball person, HORSE really won't tide you over. Same with mini-golf, and bowling with bumpers. Same with flag football. The reality is, we're applying a double-standard to fighters than we do to sports because people are more familiar with fighters, and they're broadcast to a smaller range of viewers.
That said, fighting games and tournaments are growing in popularity as they continue to grow in complexities with advanced skills, combos, and move inputs. There are top players emerging out there who are becoming familiar names to people interested. I say let it, and in time, more fulfilling simple versions of fighting games will make it out there, just like there are minigolf courses and youth-sized footballs. I don't think accessibility will be an issue at all, in the future.
And for the record, the fighting game genre likely died down from over-saturization and market segmentation. Just like there's only one major basketball league, and how people show most interest in the MLB, the genre needs to have a figurehead that represents it, rather than many brands. In the fighting genre, there were a wide variety of titles all with one type of gameplay and similar characters. It's too hard to compete in a market full of clones that cannibalize each others' business. The genre would be fine with a flagship line of titles, and lesser, simplified versions of the flagship to appeal to people who like the competition but can't play at the top level. That's better than a few new King of the Fighters, Street Fighters, Mortal Kombats, Vs. Series, and Soul Caliburs, when no individual game stands out much higher than the rest.