First, let's be clear why the seller is doing this. It's not just PayPal fees. It's the chargeback policy. The seller is seeking to avoid an easy reversal of funds if the buyer makes a fraudulent "item not as described" or "not received" claim. With direct credit card charges, the buyer would have to go through the card issuer's chargeback dispute procedure and not have the buyer protections that eBay
and PayPal collaborate on.
representative was "taken aback" only because they want to minimize friction on transactions and maximize buyer protection so they earn maximum fees. There is nothing inherently wrong or dangerous about the seller's terms.
Next, why not just phone and provide the card details. People do this with all sorts of arms-length transactions with merchants. If you are in the habit of reviewing your card account statements monthly, you'll see any improper charge, report or dispute it, and the issuer will remove it. Your card issuer also is constantly running fraud check software looking for out-of-pattern charges, and will block or alert many of those.
How is mailing a check safer than phoning in card details, or mailing card details? Your routing number and account number are printed in OCR characters on the bottom of the check. People photocopy checks, dummy up fake ones, then deposit or cash the fakes all the time. My business has been hit with this repeatedly, but our business bank always has caught them.
There is a level of concern in posts above that is unwarranted. But I realize that people tend to view these things with a high level of emotion, rather than asking what systems and checks are in place to protect them.