Well, what do they do if you drive off with the car and they have your credit card?
Your issuer is only liable for the few hundreds of dollars that the rental car company has authorized; beyond that, it's still their (or their insurance's) loss.
The only practical difference is that you're not out that money on your checking account for a few days, which can indeed be inconvenient – but arguably that's not really the rental car agency's problem?
It probably has nothing to do with getting the car back.
It’s probably to avoid lending the car to higher risk demographics.
It’s a test.
The rental car company basically loses fewer cars overall and thus has lower insurance premiums, and thus can offer cars cheaper than other rental companies that do not require a credit card (if any even still exist?) that have higher premiums to pay.
That’s the most likely theory as far as I can tell: While a credit card doesn’t make it more likely to get the money back in case the customer does run away with the car, it’s probably less likely for high-risk customers to even have a credit card.
Which unfortunately creates all kinds of false-positives, like making it very hard for tourists from countries where credit cards are not commonly used to rent a car…
Not if the issuer declines the authorization, and just closing the card (or even just temporarily locking it in the app for many cards!) would do that.
Your issuer is only liable for the few hundreds of dollars that the rental car company has authorized; beyond that, it's still their (or their insurance's) loss.
The only practical difference is that you're not out that money on your checking account for a few days, which can indeed be inconvenient – but arguably that's not really the rental car agency's problem?