The problem with using debit cards to reserve rental is the credit check. it's a hard pull. I had this happen to me twice. That's why I got into the credit game. Pulls were EQ and are due to drop Oct and Nov of this year. A big price to pay for use a debit card to reserve a car.
This is from Hertz
What kind of credit check is performed when I use my Debit Card?
The credit scoring process performed through the services of Equifax are very similar to the type of credit checks that are done when a person applies for credit.