there's a very simple solution to this for those that want to just play the "Game". cause at the end of the day it is still a game. have a level 15 quest that unlocks the duty finder for ARR after completing all the core dungeons trials etc... you revisit the NPC to unlock the next set of content rinse repeat for all the expansions (they can easily say since you did save the GCs fromt he garleans (you still have forced CS to watch for prae and the such and (you could potentially throw in short summaries of important events after certain dungeons that would only proc after completing the dungeon or trial for the first time but thats not what i would do tbh cause they may eventually want to go back and experience it in full cause all they know now is that they saved the GCs from the evil garleans trying to invade)) of course they would prolly add more ot this just using it as a placeholder for ideas sake. they hand you the quest to unlock your mount and join a GC/ability to join hunts unlocking that content and then grant you access to ishgard hearing that they're in need of help with a dragon problem (you being the hero for the GCs makes the most sense to send over) you go through the core HW dungeons/trials and return to the quest giver now in ishgard who hails you as the alliancer of man and dragon (again this can be worked on) (but he's heard news of rebellion groups in yanxia and ala mhigo against the garlemald presence there. you having already fought and won against the garleans think it's only right to head over and lend your assistance) complete the core dungeons/trials of SB then speak to the questgiver in kugane
this is honestly where my idea ends cause i can't really think of how you'd tie in STB to SHB (the only thing i can think of is you being summoned there and he crystal exarch being the "questgiver" for unlocking the SHB dungeons/raids) but my point is this is possible to do for at least 3 main parts of the story cause going purely through the dungeons/trials you can piece together a relatively basic story for each expansion in a vaccum and semi overarching like i said tying ARR to STB
of course when you unlock each new area you also unlock the NG+ for the previous expansion/ARR so if you so choose you can go back and experience the real story (which lets be real if you are here only for the "game" you'll prolly ignore anyways) but i digress while this may not be easy to implement it is a simple solution not only for those who want to straight skip to say end game but for those who want to skip parts they may consider more sloggy like post ARR just do the new core dungeons/trials it unlocks (which is more than fair imo) plus we already have systems in place to see if you've completed a dungeon before so there's no need to force a full redo of all dungeons/trials