Whaat? I've had nothing but bad experiences with PayPal, and to top it off, the only actual payment method with them seems to be credit card anyways. Also, typically when using credit or debit card with European merchants, there's extra security in the form of OTP list provided by the issuer, checked during the transaction process. I understand this is not (always?) mandatory and the merchant may be storing CC numbers irresponsibly, but the direction seems to be right. What are the possible upsides of PayPal?
I've been funding my Paypal account through bank transfers for as long as I can remember now. It is not linked directly to my debit card/bank account. This makes it impossible for any credit card fraud to happen, or for me to lose any money if any of my online accounts are breached.
It also does not depend on me having a credit card. Which I do not, because I do not require one and having one would add a fee to my account.
The best solution is iDeal, but sadly that is a national thing.
It's funny to think of cards being perceived as an American thing; I always saw the U.S. as relatively cash-oriented compared to other places. In Scandinavia you don't even buy a €3 coffee or €5 kebab without pulling out your card (the same is true in South Korea, and increasingly in Japan).
At least here (Denmark) using cards online is common. The typical card that nearly everyone has is a Dankort/Visa cobranded card, which works as a Dankort when run by Danish merchants, and a Visa when run by foreign merchants, and can be charged online in either mode. I gather something similar is common in Sweden.
The system could definitely do with an overhaul though the wording in some places was very confusing.