We have a management company but we pay a sharply reduced commission on our rents because I accept payment, collect and pay sales taxes, and generally handle everything except problems that come up when our renters are in the house.
I decided when we started doing it this way that I would take payment by either personal check or by credit card via PayPal. Is this how you collect credit cards Mermy? PayPal has its limitations and occasionally snags, but it has been useful, especially with last minute renters.
I pretty much always have at least one "live" conversation with a renter and I can tell that some of them want the convenience and others don't care. I have asked the same questions you have but I think in our case, since we fill up later than gulf front or super popular neighborhoods like Summer's Edge, continuing to accept PayPal is a good thing. I do warn renters about PayPal's "unverified" limit of $2,000, so some choose to use a CC for the deposit and a check for the final payment or vice versa. It seems to work out well.
I have considered charging a processing fee for the actual cost (or slightly less) of CC payments, but I hate nickel and diming people. It is a real cost though and I know the management companies do charge reservation fees, or at least some of them do. But often they come to me because they don't want to deal with a management company, so ...
Btw our summer weekly rate is $2385, so eventually it does add up to real money.