Thresh lantern and Teleport

With the introduction of Kalista and being able to teleport her ally with her R, I'm wondering what the thought process is of not being able to take allies with you on TP when you're thresh. Either way the champions would be suffering from the TP cooldown as kalista's ult Is on a relatively short cd. If thresh used his lantern for the TP it would be down for the fight, or atleast the first part of the fight so it has its own penalty for trying this, which leads me to the question, what would be the down side.