When I was an auto adjuster, I often ran into problems with being able to provide a rental car for someone, but not actually being able to get them into one because they didn't have a credit card.

On a side note, if you're working a rental desk and some angry dude comes in yelling about his credit score, but doesn't have a single credit card, are you going to believe him? It doesn't matter since credit worthiness isn't a direct requirement to rent a car, but just something to think about.