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This is almost like the "Monty Hall Problem", you are correct, it would be +EV to switch hands with your opponent, given that you didn't hit and you know that the other hand has an Ace also.

But most of the betting takes place before this situation occurs, when you still have the advantage. You can't not bet the flop or turn thinking this river situation might occur.

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Correct, I didn't mean to imply this whatsoever. It's just something that has taken me a while to really realize. You get to river and think "I still have TP with good kicker" but then you realize so many kickers (even lower ones now) have you beaten.

If this was a limit hand, should you then not bet this river HU? If you really believe they hold an ace than I assume so. Check/call should be the answer in position.

Plus, if you've been betting the flop and turn in position with an ace on board and villain has called, then he likely wouldn't bet any 2nd pair or lower on the river after you've checked.

Check/call the river everytime in this case?