And yeah I would be reluctant to use my credit card on a shady looking website but I don't even think twice about using my card at shady looking businesses. For example, just last week, I bought tacos from a taco stand inside gas station.
Was site shady looking or just unknown? For me as long as site has valid certs & professional UI, I am usually fine with it. Also if you are using credit card, you are not liable for any fraudulent charges.
EDIT: And credit cards still require you to reasonably show the charges are fraudulent, which means hey, you get to report it. And now you're out a credit card, so you also need to change it on all the places you need to use it.
In all cases it was also my credit card company that called me to let me know I was the victim of fraud on my card. Is it really the case that people need to hawk their accounts? I haven't had that experience for years now.