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’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.
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…
That said, you’d think they’ve considered exceptions based on your passport?
The issuer can also sell that debt (daily rental up to car value) to a debt collector.