I think this is exaggerated. Other RPG's have much higher level caps, some Tales of games go all the way to 200 and take a lot of grind to get there. I think if base game + 6 or 7 expansions wouldn't put someone off, then I don't think a Lv110 or 120 level cap would - irrespective of story that number of expansions implies that there is a lot of content to work through. I'd even go as far as to assume that most people who see a game that has 6 or 7 expansions to expect and understand why the level cap is high.
Also, for people who might only be interested in the endgame, they can always buy the skip.
ETA:
I'd also add that new players are often funnelled towards preferential servers. I'm on Raiden and the amount of sprouts who haven't even reached Heavensward but have Lv90 jobs is crazy. We have several in our FC. The EXP buff is so strong that if you're levelling one job, doing your job quests and consistently buggering about with a even a small amount of side content (like, your hunting log and random blue quests, maybe a few roulettes or something. Not some serious grind) then you'll ding 90 before you've seen Ishgard. The point I'm making here is that while new players can underestimate how story dense FFXIV is, the story is far denser than the levelling experience.