Can Apple TV estimate what time I will finish viewing the current show?
Yes.

When you tap the touch surface of the remote in the 4th &amp; 5th generation Apple TV, the progress bar appears as you described, with total length of that program along with an indication of how far along you are.



Tap that touch surface a second time. The labels on the progress bar to show the current time-of-day and the estimated time of completion. Just what you asked for.