I have looked at the conditions of a car rental company, and I believe it provides the answers:
Upon pick up of your vehicle, you must present a valid credit card (*)
used to make the booking and which must be in the driver´s name. If
you do not have a valid credit card we will accept your debit card
when you pick up your vehicle. However, as we cannot reserve credit to
cover the potential damage or refueling costs, you will need to take
SuperCover and a fuel tank of fuel at the start of the rental. We will
refund the value of the unused fuel at the end of the rental unless
otherwise agreed with you. (*) VISA, MasterCard and American Express
Credit card or Third Party Insurance IMPORTANT: In case of damage, we
will charge you the incurred amount up to the excess. You will then
need to reclaim this amount from the provider of the credit card or
third party insurer. We strongly recommend that you fully read and
understand the terms and conditions of any cover provided by your
chosen provider before you decline any of our optional services.
Without our SuperCover, should you damage the vehicle during your
rental period, we will charge you the corresponding amount up to the
excess, regardless of whether you can subsequently reclaim this amount
from the provider of the credit card or the third party insurer. In
the event you would like to dispute any of the above mentioned charges
you should send your request by mail or email to the Firefly location
state on your rental agreement.
From that, we can conclude that :
- demanding a credit card can be a pretext to force customers to buy full insurance (in this example, SuperCover) to the car rental company. The conditions state that "[they] cannot reserve credit to cover the potential damage or refueling costs [with a debit card]" ; which is utterly wrong. The customer buying full insurance will increase the revenue of the car rental company, and reduce the risk of disputes in case of damages.
- as credit cards may include insurance, demanding a credit card to the customer can reduce the risk of disputes when the car rental company charge excessive amount for damages. They can say to the customer that the credit card insurance will help refunding it.
It's likely that disputes with customers in case of damage cost a lot to car rental companies, and for the 2 above reasons, demanding a credit card may alleviate it.