Sounds like you've mostly tried 3D fighters. And yeah, they are very often based on long button strings, which, as you say, can seem really arbitrary and unnecessarily difficult. Actually, scratch that: they usually are really arbitrary and unnecessarily difficult.
2D fighters are far closer to Smash bros when it comes to how attacks work, however. Each button is bound to attacks of specific strength, and often specific properties, regardless of character. Special moves are usually done with a simple stick motion followed by a button press. Most single attacks, how you time them and most importantly how you position yourself in order to use them, are far more important than being able to string several of them together, regardless of game.
If you want to actually do manage to set up a combo at some point, however, you can usually get a functional one in three button presses, depending on the game. Or, if it's Persona 4: Arena(which is a great game, by the way), you get a decent auto-combo by mashing the light attack button. Still, they dependent on you being able to set up the situation where they can do their work, so combos are merely something that's nice to have, not anything essential.
Also, for the record, I can confirm that Smash Bros has combos. It's just that most of them are a pain to do, moreso than in any other fighter I've played. D: