In 1980, I was looking at graduate schools. I went to my local airport to buy a plane ticket and wanted to write a check. The airline wanted 2 credit cards to accept the check. My mother had to go to the airport and write the check. She only had 2 store cards. (JC Penney & I don't recall the 2nd one). Not so many people had credit cards at that time where I lived in MI.
In Austin, I wanted to rent a car. (In 1980). They required a credit card but I didn't have one. I mentioned my dilemma to someone in the Chemistry dept and one of the students said they would help me. They went to the airport and the rental agency allowed the student to be primary and me as co-renter. I did call a few days after to make sure they didn't find any damage or surprises to their bill. Would I do that today? NO! unless I knew the person very well & even then I would hesitate. I got credit cards after I'd moved to Austin and had a stable income. (however, small).
Fast forward to today. Even if agencies do not accept debit cards, one can get a secured credit card if the credit history is not good enough to get an unsecured credit card. Probably a secured card with at least a $500 limit may be enough. (>$1000 would be even better).
Getting back to hotels. Most of my hotel rentals are Priceline bidding. When we check out, we put trash in the cans, put towels on the floor and tidy up the room a bit. Usually, the room just needs normal housekeeping to be ready for the next guest.
Given there are people that will trash hotel rooms/rental cars, etc, we have no problem hotels/rental car agencies requesting a credit card.
Even Dave Ramsey would have little/no problem with only a debit card since he has plenty of assets backed behind his debit card(s).
Bottom line: I am all for hotels/rental car agencies asking for deposits, preferably by credit card.