I’m fairly certain that you are allowed to decline letting someone take your card and take it out of your sight. All the card company’s are propably even having something in their contracts that forbids you from doing exactly that.

I’d just not hand them my card

Are you stupid?

In the best case it’s gonna reduce the amount of cars.

They should couple this with the requirement to give prove of having a designated parking spot for their car. Be it a rented one or a garage on their property or whatever. You don’t have your own parking spot? No car for you.

We are legion for we are many?!

Well there are some pros in case of your buddy’s meeting once a week to play some ball. If they found a Verein, they can get a metro card and go shopping there. They can get a bank account for common costs, to gather money for a trip, to buy new equipment. Maybe some tax stuff? Don’t really know but sounds like there have to be taxes involved somehow. And they get to found a Verein.