I was inspired by how bogeymen can vanish and then reappear in front of a fleeing adventurer. The current implementation for bogeymen appears to be that "x has vanished" is a form of death, due to the text color and the fact that undead currently "vanish". The bogeyman that appears in front is probably newly created.
My suggestion is that a new movement style be added, using a token such as [TELEPORTER] (similar to [FLIER]). I'd put the code in the section that currently controls movement, so tile data, pressure plates, traps, occupancy (appearing prone), burrows, liquids, grappling/stuck-ins, etc. would be respected. All that happens is that you forego pathfinding in favor of taking a single step to move directly to the destination.
Benefits could be that certain powerful enemies could bypass your outer defenses. I don't know if that would be fun for the player, but it would certainly be Fun. Maybe we need a new, Hound of Tindalos-style enemy instead of retrofitting old ones with this power. I'd suggest that they only come to your fort once you've survived other threats for years.
Some people currently cheat to speed up the construction of massive megaprojects. If this proposed token was added to dwarves, they could move between the brick stockpile and the top of a tower in a single tick, build a wall at normal speed, and then be elsewhere a tick after they finish.
Drawbacks? Beyond this being another piece of software bloat that would be lower priority than many things Toady wants to implement, it would also be difficult to integrate with adventure mode if you tried to play as a teleporter (and people would try!).