Potential repairs on the TV are not a real issue as most wall mounts I've seen are made so the TV can be lifted off the mount. Also, most flat screens are not even worth repairing unless still under warranty.
Size of the tank would be helpful as, if small in size, two tanks with one below each aligned along the outer edges of the TV, sort of like a triangle, would alleviate most issues.
The above said I would not do this since, as has already been said, the humidity would not be good for the TV although if the TV were mounted high and the tank was on a low stand so there would be at least 3 feet between, most of the tank's humidity would probably dissipate into the room and not be an issue.
Another issue I see is that the tank would be very distracting in relation to the TV when the tank lights are on.
One more issue is the TV's audio. Especially if you use high bass settings the vibration could confuse some fish. For instance my rope fish has VERY poor eyesight, which is natural to the species, and they hunt food by smell and vibration. Most, if not all newer TVs have the speakers mounted on the back to improve sound quality as they actually use the wall as a sound board sort of like the sound board in an acoustic guitar. Even though you won't feel it with your hand this causes a large area of the wall to vibrate which would confuse many fish such as my rope. Not sure which but it is likely that this vibration would make him think there was food around that isn't or make it much harder to find actual live food.
OK, one more issue...
I'm a bit of a room decorator for my own purposes. For esthetics the tank should be the same width or a bit wider then the TV. This could likely be difficult to accomplish without doing a custom built tank which would be costly.