I wished I would be able to

(Grammar Questions I Couldn't Answer)

This question also comes off of the same sentence I've been using in the last two posts.  (This is the last question I have about that sentence).

In the summer, I looked at my friends swim at the pool and I wished I would be able to do it.

My native speaker intuition was telling me that the sentence should be "I wished I could be able to do it" instead of "would" .

But why?

Wish is similar to the second conditional--it's followed by the V2 denoting an unreal future.  So in that sense, "would" should have been fine.
The argument for "could" is that the sentence is talking about abilities.  But then wouldn't abilities be covered in the subsequent words "be able to do it" ?  So if we said "could be able to do it" aren't we saying the same thing twice?