I disagree with that.The majority of the type of casuals you're referring to don't have fun with games like starcraft, quake, or gunz.Halo has never been a great competitive game, even CE was only an above average competitive game.Which is why everyday casuals can have fun with it.
In the case of Quake, I don't think you can make the claim that casuals wouldn't have fun with it because it was already dying by the time the modern casual gamer on PC was invented. It's a decently fun game at any level if you're playing with roughly equivalent skill levels. The modern casual expects the entry into a game on a social level to be effortless, and arena shooters have never been accessible in that way because of lack of infrastructure, lack of population, or both. So I would say that Quake's failure to appeal to modern casuals is not caused by how competitive it is at a high level. There's just been no good attempt to bring them in, and it might never happen.
I don't know much about Gunz, but it looks like a game that only becomes fun when you cease being a casual player. And I think it's silly to bring up Starcraft because it's not the same type of game or audience.
As for Halo CE, I see what you're saying, in a sense. The movement skill gap is obviously outclassed by many PC shooters. The gun skill requirement is less. But the relative outcomes of engagements still have good distinction between good and great players. There are choices made for the game to be extremely accessible in omparison to those PC shooters, but the competitiveness of the game isn't lowered by much as a result, and the skill ceiling is not in sight. On top of this, the creative potential in Halo 1 destroys what Quake has for team gametypes (although it's a close call for Quakeworld), if not duel, and I would wager the same against Gunz, Unreal Tournament, and Tribes. The spawn system and grenade physics create a significant skill gap at a high level, whereas movement mechanics in PC shooters don't have a huge amount of impact on the skill gap at a high level even if the skill cap is extremely high. For instance, Smilecythe has the best movement skill in any arena shooter by far, yet he isn't at the top in any of the larger games (I'm counting Reflex as large) because other factors are more important if you want to get by at that level.
My point is, making a game accessible doesn't need to have a large negative impact on competitiveness. Does that mean I would remove advanced movement techniques from Quake to make it more accessible since (in my opinion) it doesn't have the largest effect on high level play? No, and that's because the movement helps make the game more fun at a high level, not just more competitive. And I don't think Quake would get any more fun for casuals if you removed those mechanics. Just an example.
As far as the thread topic, another buddy and I were discussing the other night what direction 343 will go in with H6, continuing with high mobility and in general "more shit", or back towards a more classic Halo. It's unlikely because of just how many damn weapons there are (and warzone variants don't help this at all), but removal of abilities aside, I really think one of the best things that could happen to the series is a drastic reduction in the weapon count. I would almost be willing to see dual wielding come back if we didn't have so many options, as I think there's some merit to less options upfront, with depth around how you combine those options (this is arguably a similar mechanic to how one chooses which two weapons they carry at any one time).
Trimming the fat in the weapon sandbox would make designing it so much easier. Having more than two or three precision weapons makes it much less feasible to make them function somewhat distinctly without wreaking havoc on the balance of the sandbox. Same with having more than one or two automatic weapons with random spread and high magnetism, or having more than one or two power weapons that give you free kills. Every sequel has more and more weapons fit into the same number of roles or fewer.