This is actually a thing and has real applications both practical and impractical. First the term "teleportation" is misleading since it's not teleporting matter rather it's the instantaneous transportation of data. Faster than lighting fast internet. Some examples:
1) Chris Pratt and Jennifer Lawrence are on a 120 year intersteller journey to their dream planet. The ship is on cruise control and everybody is in hypersleep only there's a problem and Pratt wakes up 30 years into the journey. Well he can't get any help because it takes 30 years for the SOS message to get to earth and then another 60 to get a response. If they had entangled photon communication then he'd transmit the problem and immediately get help from earth.
2) Is #1 a little out there for you? Okay something more practical. There's a an up to 20 minute transmission time between Mars and earth. Or 40 minutes round trip. The Mars rovers can't be real time remote controlled from earth. So they move a prescribed distance, transmit data back, then they tell it where to go next. Of course we've seen movies where when astronauts actually travel to mars all the problems they have communicating with earth when they encounter problems like aliens etc. If they had entangled proton communication they's be able to warn the earth of the alien invasion 20 minutes earlier.
3) How about here on earth? Remotely piloted drones. Yes we can fly them over Iraq from safely in the US but there is actually a several second delay in response to control inputs. In fact the drones are launched and landed from closer locations for that reason. If they had entangled photon communication that wouldn't be an issue.
So by now you can probably think of a few more applications where instantaneous communication would have practical benefits.
4) Here's one you may not have considered. Encryption. Since the message doesn't travel over any medium it can't be intercepted. If it can't be intercepted it can't be decrypted. Who ever owns the technology first (and for ever long only they have it) will have a one helluva military advantage. I suppose a corollary to that would be jamming. There'd also be no way to interrupt transmission.
At least, that's how I understand it.