I prefer to use PayPal to pay at random sites just because I'd rather not give my credit card number to a site that could be backdoored or even run by fraudsters.
But I can call American Express, be instantly connected to an agent who at least pretends to care, doesn't sound like they're overworked, and will gladly put in the chargeback request for me. I can also do this online if I'm feeling less social that day.
You're right about PayPal helping themselves to bank debits. I have a small eBay business and back when they dealt directly with PayPal, I would have a separate account to receive the funds and as soon as they hit I would transfer the money out. It's just part of the OPSEC that's required when dealing with our new megacorp overlords.
The email the bank sent me to prove 'I did it.' -- something very close to 'piratearrgghhhh34398903@yahoo.com' The fucking scammers taunted me by literally calling themselves pirates in the invoice. The one upside of paypal is the customer basically always wins to the point you're almost relying on the good faith of the customer not to take the money back.