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.
In Germany the acceptance for credit cards only became large scale after the interchange fee was limited. Today, most stores that accept card payments also accept credit cards, but only MasterCard and Visa. Using an AMEX as your primary card would be a pretty bad experience, because you'd constantly need a backup.
With that said, I'm happy most merchants don't put up with the humongous fees—in the end the prices are just raised to compensate for them.
Same in NZ. People who work for more... insular... American companies here are regularly embarrassed by being unable to use their corporate card (because e.g. IBM mandate Amex) most of the places they go.
1% for spend under 10k, 1.25% beyond on the Amex Platinum Cashback Credit Card.
Combine that with the fact that Amex gives targetted cashback offers I can well believe you can end up averaging several percent on a yearly basis if you're taking up some of the higher value ones (I currently have an offer for £100 cashback for £1000+ spend at Trailfinders, that would bump my average cashback up a fair bit!).
There are higher cash back cards also the cash back is usually capped on a monthly basis rather than on a flat %.
So far for this year I have £341.92 cash back on the card.
Mind you that this isn’t a new card I had it for 5 years.