I agree that 90,000 crystals is a long haul. Napkin math + guessing incoming!
Not counting limited crystal sources (story, dailies, free missions) You don't really get a lot. Each month (30 days lets say) you will get 6 single draw tickets (1 from daily log in (every 15 days) and 2 from the cross app promo ( I think every 15 days?)). These same sources will give you a combined 2 rolls in crystals per month (I forget the exact amount, but more than 600). That means from just logging into stuff, you'll get 8 rolls per month.
Looking to events, we have Guild Wars every month, and 1 or 2 other events. GW alone gives us 300 crystals just for clearing each of the difficulty levels. I won't count the random chance ones from the token draw since I won't make assumptions about how people grind. Other events, like the current Miscoloured Memories event, Give about the same just by clearing the story + raid battles. None of this includes trophies either, since I never pay attention to how many crystals I get from those (I'd assume around 100 though).
So, all in all we get 10 rolls per month if we do all of the things offered. That would take 30 months (2.5 years) to get the full 300 rolls needed with just the regular sources.
As for the story, we get 50 crystals per story mission, and 4 story missions per island. Each story mission comes with at least 3 free missions normally, each giving another 50 crystals. I'm up to chapter 33 right now, and I've only done about half of the free missions open to me, and I do all of the event stuff. I've spent about half of the total crystals I've earned, so I'm looking at having made around 16000 crystals so far? This does include trophy stuff, extra crystals given out by the devs (around 1800 I think), those monthly sources above, and token draw crystals though, so it would be inaccurate. I would guess a player should be able to get at least 18k crystals if they did the same story progress as me, but kept up on free missions and on all events. I've also not done most of my fate episodes, which give 50 crystals per character you have. That is 60 rolls from the time grinding limited sources. That would cut off 6 months from the total grind, but you are still looking at around 2 years of saving. Even if we add in all of the other sources of crystals (except developer gifts, since those are apologies/totally random) I didn't, I would assume we are still looking at 1.5-2 years of saving crystals + roll tickets to make that 300.
I mean, I did a lot of guessing and stuff to get where I did, but I think it should be accurate, if maybe a bit generous. If you get lucky, you can cut that time in half by investing on a completely broken character launch and hope to get it all back, meaning that you could totally get 300 rolls in a few months without spending any cash, but I think after 2 back to back broken launches they've learned their lesson for a while. Either way, you should be able to get at least 10 draws per month, and around 60 draws from the story and missions. Also, as you make those 300 rolls, each character you get is another 50 crystals, so assuming you get 1 per 10 roll that would also give you another 5 rolls. Still, seems like a far off goal for very little pay off.