> You can reverse the charges on debit cards, but the money is withdrawn at the time the charge is made. This is not the case for credit cards.

In a sense it is though, because it lowers your available credit by the amount of the charge. And the fraudsters are going to try to run you right up to your credit limit, so you end up at the same problem: You now have legitimate charges being declined because the fraudsters locked up your payment card.

Having multiple credit cards in the US is quite common, since there's no practical downside (unlike having multiple checking accounts, which locks up liquidity at usually no interest payment) and it can even be beneficial for your credit score.