Fast travel Daggerfall style didn't hurt my immersion, but fast travel Morrowind style really did.
For one, the mages guild travel was lore breaking from the previous game. The silt striders took you anytime you wanted to go, and your fee could never justify the expenditure of time and feed to maintain the creature. The fishing boats couldn't catch enough fish in a day if they had to row you up the coast and back for ten bucks. The proplyon chambers were alright, but didn't take you anywhere useful. The Intervention spells didn't require any religious affiliation, you could spam them to travel between cities.
If the fast travel methods of these sorts actually made sense in the gameworld, there would be a lot more to stand on in terms of immersion.
To not break immersion, to me atleast, it simply has to be possible, in morrowind it would be possible t ride on the back of a siltstrider, or take a boat somewhere, it is on the otherhand not possible to teleport to anywhere on the map at any time from anywhere. And even if you want the cost to make more sense in terms of giving it more "worth" sure I'm not against that actually, but it would still be the same system, simply balanced.
Now I never played daggerfall enough to getout of the starting dungeon (I just can't get used to the combat mechanics), so I don't know how it worked, but IMO morrowind has been the best system so far.