

No, I think that you have that right for every contract, that you enter (buying contract or otherwise). Though there are exceptions (for example digital goods like ebooks). Ypu can very much bring back a retail good that you bought in a store for 14 days after the purchase. Though I think they can refuse, if you damaged the product in that time.
For example I returned an item I bought in the tool store, because I realized I bought the wrong one.
Thats why other countries are doing it that way. The problem is, that the US system makes it very difficult to get an ID for its long list of undesireables. And with that I mean everyone, who is not white, heteronormative, cis and not-poor. If the US fixes these problems and issues IDs for every of its citizens, then requiring the ID for voting is a good idea. Unfortunately that is a big big If, carrying a lot of weight.