A quick check on google gives the following results:
- "I wish I would have" - 5,080,000
- "I wish I had" - 19,900,000
Okay, so the nonstandard construction is indeed less common, but only by about 4:1. And five million hits is enough to question why people use this construction. Saying "that's how they learned it" isn't explanatory, because this just shifts the question back a generation, to why their parents said it that way, ad infinitum. My bet would be on the desire for a different construction marking the protasis of a conditional clause (the protasis is "if" clause of a conditional construction; the apodosis is the "then" clause). While language does tend to eschew redundancy, there are so many cases of redundancy in language(s) that this is clearly a constraint which is readily violated. The phrasing "I wish I had gone to the store" is perhaps a bit puzzling if we take out the conditionality. Why "I had gone to the store"? Why not "I have gone to the store"? After all, it's a wish about the present situation. This may be why some people prefer "I wish I would have gone to the store", because it's transparent. "I would have gone to the store" makes more sense out of the subordinate context, and simultaneously shows the conditional/irrealis nature of the wish in a way "I wish I had gone to the store" does not.