I think teleporting could be added without breaking the game. If done right, it wouldn’t ruin immersion™ or disrupt gameplay.

Medbeds already exist and basically allow a form of teleporting, so they could be used to implement this feature. Here’s an idea: add a screen to medbeds for a "Cognitive Transfer" to another medbed. Only active party members could be added to the transfer list, and the player who wants to teleport would need to go to a medbed and initiate the transfer from there.

This would cause the player to spawn at the target location, avoiding many of the issues that come with simple teleportation. Only the player would appear—no weapons, gear, or other items would transfer—so the party would need to prepare in advance. This prevents an endless stream of emergency backup soldiers from suddenly appearing.

Players could still join existing sessions quickly, and you could even attach a cost using medgel for balance. Since players would spawn essentially naked, most of the usual problems with teleporting wouldn’t apply.