Some car rental companies do prefer a credit card (Hertz and Avis). I have used Enterprise in both UK and USA, and they are quite happy to accept payment with a Debit Card. Every time I have rented a car in UK and USA from Enterprise I have used my Thai driving license and paid with a debit card.
I have a 5 year Thai driving license. I have hired cars in both UK and USA with it. No problem at all. All the large car rental companies are used to seeing foreign licenses, all totally routine. All they require is your license and your passport. They may ask for a local contact address and phone number. No need for IDP.