I think some people might be beyond help but the MSQ does force players to learn the game. You are forced to do a lot of dungeons and trials as part of the MSQ.
So does someone skipping all of that have a potential effect on my enjoyment of the game? Yea, it does. I don't want to queue into max level content and get paired with someone who has no idea how to play the game. "Hello, it's my first time here" and "hello, this is my first dungeon ever" are very different things. Just pause for a second, go back to the beginning of 3.0, and imagine the immense frustration of having Dusk Vigil be someone's first dungeon ever. Imagine Ravana being someone's first trial ever. The player-quality floor for DF and PF on NA and EU servers is already hilariously low. Letting players leap straight into the end-game would drop it straight into the seventh hell.
New players are important. But, when your new players would rather skip your content than play it, that says something about the quality of player joining your game as well as the quality of your content. For an MMO, player progression should also be a bond you form with the world and your character. For someone that experiences the MSQ, they defeated Ifrit and Garuda. They are Titan's bane. They are a Scion. They are the friend of Haurchefant, Ysayle, Aymeric, etc. They are the Warrior of Light. For someone skipping everything, they are just a random max-level PC. When no bonds exist, they can leave the game just as easily as they joined it.
I've said in the past and I'll say it again. If they want to make the game more accessible then they need to condense and polish up the MSQ. There is a lot of completely unnecessary fat that can be trimmed down. Get rid of all the go-between NPCs that serve no other purpose than to make your journey a few steps longer and just get to the point quicker. Get rid of a lot of the fetch quest garbage nobody likes. Remove a lot of the unnecessary dialogue. Give players access to mounts or faster movement earlier on. Perhaps even cut out a redundant dungeon here and there -- the progression between Sastasha and Copperbell is not that large from a player development perspective.