Stripe did introduce Stripe Atlas. Although this doesn't solve the situation totally, it's at least one of a number of helpful steps in the right direction.
If you want to register and run a us entity it helps but most people don't want that kind of hassle. I've done it from Canada and Australia and unless youre planning on getting us investors is probably not a good idea. Though I haven't accepted my atlas invite yet so not sure how much better it'd be.
Sure, but that's not what we're talking about here. For those kind of payments, in the US they still tend to use cheques. For buying stuff from shops or online, we use cards, just like anywhere else, no?
If you mean you use credit cards for buying stuff online, then no: that is not what we do here. I'm not sure about all of the EU, but at least in NL the majority of online transactions use payments directly with your normal checking account at your bank using a system called iDeal (see https://www.ideal.nl/en/ ).