Ah, it's that time of the day again...
Morrowind did have fast travel. Between the siltstrider, the various mages guilds, mark-and-recall, the Intervention spell, the propylon indices, you had plenty of means of travelling fast. The only difference is cosmetic, yet important : there was an in-game explanation for these. Think of it that way : would you rather fight your enemies, or just console their deaths in ? Same result both times... But the mean to achieve it in one case is immersive and believable.
So, I don't really care how : spells like mark-and-recall, go to a, errrr... tame bear-riding station ?
, quest to get access to it like it was for the prolylon indice... As long they explain it.
And given that I seem to remember that one of the thu'um shouts teleports you, I think they just might.