Couldn't the rental car company keep charging the card and the issuer remains liable for further amounts?

Exactly this.

The issuer can also sell that debt (daily rental up to car value) to a debt collector.

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.

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…

It does but I assume the loss of business from foreign customers still is less than the cost of losing cars.

That said, you’d think they’ve considered exceptions based on your passport?