Let me say first that I'm sure it's possible for someone to swipe a card and keep the number to swipe again later. I wouldn't consider seeing anyone that isn't well reviewed and has plenty of history here so I'd feel safe that wouldn't happen.
I understand the basic reasons why credit cards COULD be a bad idea - like if you're married and have someone who has access to them or the risk of having the number stolen. I get that. Is there something I'm not considering and are credit cards widely accepted?