Which is actually an absurd thing for the rental companies to do, since they a) don't know the credit limit on the card and b) would immediately get a chargeback if they tried to recover anything beyond the actual rental rate. They would fight and have a not totally unreasonable chance of winning the chargeback, but the reality is they'd be far better off chasing you down with collections agencies.
People walk away from a cash deposit more easily than a credit card.