>Also, capping the interest rate doesn’t reduce the benefit to making encouraging people to spend and carry debt, so I doubt they’ll go away.

That is exactly what it does. The benefit to people carrying debt is the interest they pay. If you reduce the interest rate, you reduce that benifit.

> Credit card reward programs exist to encourage spending on massively over market interest rates.

More charitably, they exist to encourage you to spend what you'd spend anyway, but on their particular card.