I can't see them ever doing an officially sanctioned in-game parser or other sort of "performance checker" or "grade" that's available in actual content and visible to the whole party. Regardless of how much people say they'd use it with total nobility, it'd undoubtedly lead to performance-based harassment and exclusion. We already have a situation where "no bonus" parties pop up on PF within a day of the content becoming available, and it gets harder and harder for new players to get clears as fewer and fewer people becoming willing to take a risk on an unproven player. If you give people the power to increase their own success chance by excluding others, that's absolutely what they will do.
I think that more should be done to give players feedback on their performance or encourage them to improve, but giving players the ability to stringently vet each other is just a can of worms I can't see Square ever opening. It's dehumanizing; it's treating other players as accessories in your own success instead of real people.
To try and improve player performance in general, there's a few things I think they could do. One would be to simply require the completion of the corresponding SSS/CoS dummy before the game will even allow you to queue for high-level duties. The dummies don't measure absolute performance in a raid setting, and don't deal with mechanics, but they are a reasonable test of someone's ability to perform their rotation to a "good enough" standard. Clearing the dummy shows you are at least willing to learn your rotation, and have the ability to execute it, which should be enough to verify that clearing the actual content is within that person's reach. Because it's the game itself putting up the barrier to entry, rather than the players, there's no risk of exclusionary harassment on the players' part, and the people who struggle to clear the dummies can reach out to the community for help on how to improve. If someone is unwilling to try and improve they never have to come into conflict with actual players, they simply can't access the content.
The other thing they can do is try harder to teach players how to improve by offering better in-game resources for learning. Hall of the Novice doesn't even scratch the surface, it virtually doesn't teach anything that you won't be forced to learn simply by playing normally. The game does a very poor job of informing players of how to play properly. There are things which seem obvious to an experienced player, like the difference between weaponskills, spells and abilities, and that you are intended to use abilities in between weaponskills/spells. Yet nowhere in the game (or in any official materials as far as I'm aware) is this told to the players. Similarly, you are never told that DoT/HoT effects tick every 3 seconds. Without that knowledge you have no way of calculating how much these effects are worth, which means you can't effectively plan a rotation. They simply expect you to realize on your own that DoTs are almost always worth it but should only be refreshed when they're about to fall off.
Or how about how there is NO in-game information on whether damage being dealt is physical or magical, or if it's piercing/blunt/slashing, even though there are many skills and attacks which only affect certain categories? Are people really expected to just realize that Elixir Field is blunt damage, or that Shield Swipe is slashing? Some tankbusters are obviously physical/magical in nature, but for others it could go either way. Take Mustard Bomb for instance. It's magical, but it could just as easily be physical, the only way to know is to either run 3rd party software or do tests to see if the damage is reduced by Dark Mind or a parry. On that note, the game also never actually tells you that magic damage can't be parried.
It's frankly ridiculous that information THIS important can only be discovered by consulting external resources. And that's just the really obvious stuff, it's not even getting into the matter of things like rotations or openers. If a player wants to improve their performance in this game, it is absolutely useless for them to look within the game itself, they have no choice but to reach out to the community. Not everyone is going to do that. It shouldn't have to be that way. There is absolutely no reason why basic, critical information on combat and how certain jobs are intended to be played, cannot be offered in-game. Even if it's only in the form of text dumps instead of proper tutorials, that's still better than absolutely nothing. That alone could do a lot for raising the average skill level of the playerbase.