How could the credit check keep quality high? It's not going to change who I can accept payment from since the payer doesn't have any connection with Square. Square isn't lending me any money that I somehow need to pay back when I accept a payment. So... why check my credit again?
My understanding is that they use it to verify your identity and it's also used to set your daily and per-transaction limits. My guess is that this is just fraud prevention and a way Square can keep scammers off their service.