Often times feedback is best left anonymously which allows the honest truth to come out. We run a home services company and have experienced this sentiment. Our customers won't likely leave a review for our contractors unless it couldn't be traced back to them. It's a bit different from Square but nonetheless, it's something that should have some sort of effect on Square's end.
Square isn't soliciting reviews for the small business, but instead private feedback. Should the customer subsequently go out and write a review (anonymous or not), the thought process is that the review may be influenced (hopefully positively) by the customer service.
This is a proactive approach to customer reviews as opposed to a reactive one.