Nothing, except that then their card would have 0% acceptance.

Much harder sell to get people to get the card if no merchants accepts it, and harder to get merchants to take it if nobody has one. There's a reason why the credit card market is almost entirely American Express, MasterCard, and Visa.

If they wanted to pay higher cashback than the standard interchange rates allow, they'd be charging merchants more than they're charged for accepting MasterCard or Visa, which means you'll end up with at most spotty acceptance like American Express.