Considering you are swiping, signing, and getting a receipt for your payment, I think it would be challenging for a lady to take more than authorized. It would also be terrible for business and reputation.
Any lady who does accept credit cards has to be together enough to have registered a business, be paying proper taxes and GST for all of our liaisons, have gone through the trouble of setting up a merchant account and paying all those applicable fees, as well as all the credit card fees etc. It's not going to be your fly by night ladies that accept credit. It will likely only be well established, put together and honest ladies (or agencies). If we are honest enough to declare our income, do you really think we are the type of people who would steal from anybody - much less the very people who we share intimate times with and who provide us with our income?
Yes, there is a paper trail, but that's not a problem unless somebody is already scrutinizing you. And if that is the case, large cash withdrawals will probably be more problematic.
Besides, any lady who does accept cards will have an industry neutral and discreet business/billing name that would never raise eyebrows.
With that said, if you are seeing dodgy ladies, or somebody without a good reputation (yet), then you may not want them even knowing your name.
I don't know, that's not my demographic. I almost never receive cash (5 times in total this year), so it never even occurred to me that somebody would think along the lines of poonman.
I'm sure he has valid points for some people, and I'm not meaning to minimize his comments. I just don't see any greater issues with it than swiping your card for any other reputable business.