… For example, the Bat Signal can be exchanged for Batman on my turn, but couldn’t the other person just trade it back on their turn?

A: Yes, the Bat Signal is straight-up traded for Batman (or Stolen Goods/Garak can be traded for certain other Keepers as well) and your opponent could choose to simply exchange the two cards back on their turn. While this may seem slightly pointless, there are a couple of reasons this would be useful.

The optimal use, of course, would be to use your trade-forcing Keeper to get possession of another Keeper you need in order to win the game, in which case, future trade-backs would be moot. Batman in particular has some other useful qualities, like the ability to trash one of your Villains. He could then go to back to other parts of Gotham on your opponent’s turn, no skin off your back, especially since, should you need him on your next turn to trash another Villain, you could exchange him back again. (In the case of the Bat Signal, think of it as being able to have Batman on call whenever you need him (on your turn). Sure, this keeps Batman running all over town, but, hey, he’s a popular guy!)

Trade forcing cards other than the Bat-Signal include:

Stolen Goods (Firefly Fluxx) which can be traded for any other Keeper in play except The Serenity.
Garak (Star Trek: DS9 Fluxx) who can be traded for any other Visitor / Station Personnel in play.