Personally, I can't think of any non-license FPSs that have a deeper story. Half-Life doesn't even have a story. It has an opening sequence. Lotsa monsters. Then an ending movie. Half-Life 2 I haven't played enough to give an accurate summary. FEAR falls into the same category, but with movies at the end of each level. Condemned TRIES to have a story, and would've, but ended up not having it fleshed out or even completed because it was a launch title that was noticably rushed.
The only FPSs with bona fide stories I can think of are the likes of Goldeneye, Nightfire 007, Star Wars: Republic Commando and the like. And all of them still rely on established mythos and recurring themes from their source material. The fact of the matter is that very few people go into an FPS expecting a deep, sprawling story. And with very few exceptions, they walk away disappointed.
Halo 1/2 doesn't have a deep, epic story. It's pretty simple with a standard inexplicable invasion by the Covenant who worship the Forerunners, a mystical pre-historic species who were wiped out by the Flood, which results in the Spartan program, leading to the big MC (my nickname for the Master Chief) saving the day. Then the Elites split off from the rest of the Covenant because of the Brutes seizing power over them, leading to a genocide by the Brutes, while the rest of the Covenant attempt to activate a Halo, blinded by a falacious feeling of safety because of blinding from their religious beliefs. Simple, right? (It is).
Half Life 1 has an evil corporation who opens up an interdimensional rift, for some reason, that leads to the apocalypse. Then they freeze Gordon Freeman. Better known as the floating hands that hold your gun. Most of his character development comes from the instruction manual.
If you're looking for a story, with very few exceptions, you're not finding it outside the RPG. Notable exceptions being Metal Gear Solid, Starcraft, Warcraft and Mega Man (there are other exceptions, I just can't think of any atm). Outside of RPGs, the vast majority of games, Resident Evil comes to mind in particular, require you to piece together the stories yourself via in-game books and unlockables. You can complain about a game not having a story, or having an over-rated story. But really, the tier drop when it comes to stories is colossal between those top-level stories and everything else.
To put it simply, the rankings of stories go RPGs, MGS, etc>>>>>>>>>>>>>>>>>>>>>>half of everything else>the other half of everything else
Next to fighting games, the FPS genre is easily the most-lacking genre for stories.
Single player is indeed done better in a lot of games. Halo's biggest weakness is easily in its "all alone" idea. It's you versus everyone else. But it doesn't give you that sense of loneliness and fear that Condemned, or even Metroid Prime gave you. It doesn't have that squad-based gameplay that lots of tactical shooters like Ghost Recon and R6 have. Halo would have this if the marines weren't just plain pussies. Other games, like Splinter Cell, make up for this with raw gameplay and sheer diversity between levels. Halo 2 also misses on this, outside the transition from a temple to a space station to a hilly forest back to a temple, then to a snow level (in all seriousness, every game needs a snow level).
What Halo DOES have is the sense that you kick an enormous amount of ass. The door opens in front of you, and then everyone runs for cover because they know what a badass you are. If it was one of those wimpy-ass marines back there, undoubtedly smeared across the walls, they'd just open up and he'd be dead. But no, it's you, so they run and hide. You go from place to place. You kill everyone. You jump on their ghost, crack em in the side of the head, steal it, run them over with it, then kill more people and they can't hope to stop you. Bring in a friend and do co-op and it's even better. You roll out like Brett Favre, dodge a warthog that got jacked by the Flood, then stick them with a plasma grenade and watch them light up (I'd say you roll out like McNabb, but then you'd throw it and it would land like 10 feet in front of them). It's not like Medal of Honor, where if you stand up at the wrong time, your head gets taken off, or Splinter Cell, where you fall five feet and die. It's the only good game around that you can just go head-to-head with a tidal wave of enemies, kill them all, then get complimented by that stereotypical black CO I don't remember the name of. Really, Halo is the only good non-realism-based shooter still around. So couple the appeal of being able to simply kick ass and the best online multiplayer of any shooter on a console (and I've heard people make strong cases that it beats out CSS and AA as well) and there's really no reason Halo shouldn't be widely beloved.
And bad AI? What game doesn't have AI that can be exploited? How many times have you jumped on top of a rock in Oblivion and whipped out a bow? Or find just that right angle behind a crate where they can't get a shot to hit you, but you can cap them, no problem? Or that hallway where you can bait-and-switch ten enemies to go through a doorway one-by-one? In all seriousness, you could take any video game ever and find a way to just dispatch the AI in an entirely unrealistic way.