Yeah, violent games and shooters have been around well before Halo. It just brought shooters to the consoles. God forbid other "bro types" enjoy games too. There's plenty of other inventive, creative games out there if that's your thing too.
Being a bro isn't, like, something you're born into. It's a certain mentality, a certain way of approaching the world. And while I like many facets of bro-dom, and enjoy the hell out of sitting down for some Smash with a couple of friends and a six-pack of Yuengling, there are some bothersome things about bro culture which that particular category of game emphasizes.
I mean, I'm critical of the FPS as a genre to some extent. It's fun as hell, but the nature of how the genre's set up has given it some kind of crappy limitations that no game I know of yet has managed to overcome. Even the best ones, like the Half-Life franchise, are limited in ways that bother me. I'm also not super fond of hardcore gaming: it's cool to watch from afar, but it's not an especially inclusive culture, and I fear that games like Starcraft and League of Legends help to scare away a broader variety of players. I'm not trying to say that gaming was perfect before Halo came out; I do think, however, that Halo helped to push a wave of bright designers in some shitty directions, and that game design has suffered as a result.
I'm critical of "games that attract waves of bros", if the bros seem to be the majority of person attracted to a game, in the same way that I'm critical of movies that attract that sort of person. Adam Sandler movies, for instance. I'm not saying everybody who likes Adam Sandler is a bad person, but I do feel that Sandler movies are kind of puerile and limited in a way that appeals to a particular type of person, and that, to the extent that they influence other creators, they do some damage to our culture. Adam Sandler's influence on movie-making has been less impactful than Halo's influence on game design, so the mentality described in the OP does bother me somewhat. To hear a guy working at Microsoft say "my company specifically tried to manufacture this kind of experience to reach this kind of audience" pisses me off.
It's quite wonderful, and now I'm thinking about what the equivalent for Halo would be. Maybe a game that brings out the tragic aspects of war -- not just as shocking gore, but as sadness and horror. Maybe a game about a Halo warrior's post-war life, a civil Sim-type game interrupted by disturbing scenes of post-traumatic hallucination & paranoia. Or a game that starts out as a shooter and becomes impossibly difficult, until the player's inevitable death, after which the real game begins, taking place in a Tibetan Buddhism-inspired series of post-death liminal states of terrifying scenes of his past sins.
I think the key to understanding "how to do the FPS better" is that the first-person model doesn't only have to exist for shooting. It's a very potent set-up because it's "virtual", and limits your perceptions to the scope of the character you're controlling. You could make a game that involves guns but is not strictly a shooter, and therefore has the freedom to give you a certain context into what surrounds your actions.
As much as I love Buddhism in my video games, I feel like your idea might feel too preachy to your average player. But how about this for a set-up? The game starts off as a "sports" shooter game – say, paintball, or something of the sort – and you're a person with a couple bucks and a passion for the game. Ultimately, you get to a point where you're up against people with much better equipment than you, and the game becomes almost a test of masochism: how many times will you try before you give up? But there's a whole other world out there, offering you opportunities to make a quick buck. And whether you pick a live of military service or a life of crime, you're put back into a situation with guns, only now the stakes are infinitely higher. There are no second chances.
A game like that could really play with character development, both by looking at the people who serve along with you, and by making enemies something more than faceless soldiers. Give you the impression, perhaps, that the only people fighting these fights are people who don't have the idle money to play paintball all their lives, and that you're being sent to war against yourself, against people who are pretty much just like you. Except that sometimes, you're fighting for the rich people who want more, and sometimes you're fighting as the underdog, against a group of greedy people who are willing to use violence to get what they want.
Of course, if you're looking to avoid that kind of morality, you can always stick to playing paintball. But you're aware of the fact that even there, you haven't quite escaped from the world as thoroughly as you may have liked...
I know nothing about paintball forgive me
This is of course completely lost in multiplayer, but I'm not sure how you can blame bungie for the non-authored parts of the game.
The story of a game is told through gameplay, not through cut scenes in between. The gameplay of Halo is, "kill these things". Not much more complicated than that. The writing can self-pity itself as much as it would like, but the fact remains that Bungie created a game in which there is only one possible course of action, and that is to kill. That multiplayer is such an aggressive shitpile, legendarily so in Halo's case, only goes to show that beneath the facade of "story" in Halo, there is pretty much just "shoot things and feel like a badass for doing so, or else get pissed off that somebody is better at shooting you than you are for them."
Jonathan Blow, who's a brilliant game developer in his own right, gave a lecture in 2008 about exactly this sort of dissonance between storytelling and gameplay. He does a great job pointing out that even the best titles in gaming, like Grand Theft Auto and Half-Life, do a poor job of aligning in-game story with the actual play. It's long, but if this is a subject that interests you, then it's absolutely worth giving a look: http://www.youtube.com/watch?v=mGTV8qLbBWE. (Whilst studying this subject for my undergraduate thesis, I also took notes on this whole lecture, so if you're feeling lazy I could upload them for you; let me know if you'd like that!)
Last year's Spec Ops: The Line did a lot of this kind of work, subverting the FPS genre while you play through it. Zero Punctuation's review of it is insightful as usual: https://www.youtube.com/watch?v=HNhPMjbgkXA
People who say "Adam Sandler Movie" usually think of movies produced / written by Adam Sandler.
I used to love playing Halo 1 over system link with a group of friends but now trying to hop into Halo 4 only to have a bunch of kids cursing at eachother it turns me off from multiplayer. I agree with you in that some of those elements from the hardcore competitive culture are disappointing, but that is just one facet of gaming culture as a whole. I still feel like there's plenty of other good parts that it doesn't bother me.
What makes you think League of Legends is a hardcore game, particularly compared to Starcraft?
I really don't see it scaring people away from video games; it is one of the few RTS/ARTS games that have gone for mass appeal instead of gratuitous complexity. Honestly, I think it rivals even MMOs like WoW in how friendly it is to new players, which is reflected in how many people have moved from WoW to LoL.