Combat absolutely gets much, much more complex later into the game. Once you hit 30 and unlock your job you'll be given a suite of new abilities, and from there things just get more complicated. How many "buttons" you'll have to push will depend on your job, but a big part of the later-game combat is working around the 2s global cooldown that's on most abilities, and "weaving" non-GCD abilities between those 2s. You'll also soon have multiple meters to keep track of and work around.I'm going to say upfront this is question will rub some people the wrong way, but when does the gameplay get a reasonable level of depth to it?
Me and my buddy started the free trial today and after a good 15 hours between the two of us, we both have the exact same complaint. He's a level 16 conjurer and claims to only have two attacks (one of which rarely works). Yes, the conjurer is a healing class primarily, but it seems like they would still make it decent to play solo. I don't feel much different with my level 10 pugilist -- I hit B, A, X on my controller to do my little song and dance... and that really it. I'm a decent ways from getting any skill that seems like it would disrupt that progression; even worse, I haven't gotten an inclination that it's going to stop working for tens of hours.
I know that I'm still "early" on in the experience, but the thing most people complain about with the base game aren't bothering me. Yes, there's a lot of menial tasks they're having me do, the map system is confusing at best, and the lock-on system really ticks me off, but I'm enjoying it. The world feels inhabited and the writing seems great. The aesthetic of the world also impresses me, despite how dated the graphics are. But like I said, unless the combat gets significantly more involved (on a per-player basis) it's hard for to envision spending an exorbitant amount of time with this game.
We aren't MMO people, is this just part of the genre?
If you're curious to know what your jobs might look like in the future, I'd recommend looking up a rotation guide for that job and see what that looks like.