Reasonably fast mounts aren't a problem, but teleporting is. Mounts and vehicles -- if implemented carefully -- add to a world by giving players interesting choices to make.
Both super-fast vehicles and teleporting fail that test because they take the "interesting" out of "interesting choices." When a feature is all plusses and no disadvantages (and costing a lot never remains a disadvantage for long after the game launches), there are no choices to make! When there's an obvious "best," everyone who can will always take the best. El yawno.
Mounts and vehicles need disadvantages to balance their advantages. I don't mean gimping them in some obvious way just to quickly solve a gameplay problem; I mean limiting their utility in appropriate game situations so that there's rarely a "best" solution in all cases.
For example, let's say there are four main modes of travel: walking, mounts, vehicles, and ships. Walking can take you anywhere on land, but it's slow. Mounts can move you on land faster than walking, but can't negotiate steep terrain. Vehicles can go very fast on land (and some might be able to go slowly on water), but can only travel quickly over roads; in other terrain, they're not much faster than walking (but they can carry more stuff than a person). And ships can go relatively quickly over water, and can carry big loads of stuff, but can't go over land and are subject to being blown off course (this last might be optional).
This creates a system in which not everyone is traveling in exactly the same way because some travel options work better than others in different situations. People get to make interesting choices based on their goals.