For me the attempt at variety is what killed SA. I just wanted to do missions, not menial crap like sitting in a gym tapping the buttons because my player apparently atrophied all of his muscles running around, or being warned that my girlfriend is sad because I wanted to actually play the game instead of carefully driving her to a restaurant and back, or some pointless turf war that I'm going to die in because the game has given me hardly any weapons. I know you didn't need to do all of that, but it nagged you constantly with that crap, and I was getting no payoff from the missions either.
Gah, just thinking about that game makes me mad. They tried too hard to add something to the game, and went completely the wrong way about it, and ended up just bogging the game down with stuff I don't want to do that completely detracted from what makes those games fun.
The fact that the muscle and stamina skills took so long to get up, and then could actually decrease, greatly annoyed me aswell and was probably my biggest gripe with the game. That is, until I applied a mod that prevented either skill from ever decreasing again. PC master race.
The girlfriend thing, I don't remember being annoyed by it, though my memory is probably foggy. After being introduced to those mechanics in a story mission I don't remember ever having to do that stuff ever again, because you didn't actually need to do that unless you wanted 100%, but why bother going for 100% if you can't stand half the things you need to do to get there? I certainly don't bother. The dating game doesn't appear as part of the story again until one mission later on where you had a choice of dating a girl over and over to get something from her, or killing her and taking it. You can probably guess which direction I went in.
You don't get nagged about turf wars either once you leave Los Santos, and you don't have to worry about it again until the last part of the game when you return there. By that point you have so many weapons and so much ammunition that they become fairly trivial to do. And, IIRC you didn't even need to take over every neighbourhood to unlock the final mission, just a certain percentage of them.
Though if you're playing on a console, the muscle/stamina thing could very well be reason enough alone to not ever play it.