Doesn't Apple wallet require contactless payment?

It's my impression that contactless payment methods are not as common at car rental places as at "everyday" merchants, but that may vary from place to place and rental company to rental company. So you may need to figure out if the specific rental counter you'll be going to can accept contactless payments.

You typically need to bring the card to the counter if you don't already belong to a rental car program where you preregistered the card online and already used it for a rental before. But even if you preregister the card online, the first time you use it in many car rental programs you have to physically show it, not necessarily because they have run the charge on the physical card, but likely because they have to compare the info you entered with the info on the physical card. If Apple wallet doesn't show both sides of your card to full detail, then Apple wallet may not work for that.