Here in small country in EU, Czechia, we have several payment processing companies, which process debit cards payments online.(nobody use credit cards here, spending money you don't have, no thank you, rofl)
These are companies based in our country, you can call them, you have a written contract with them, so if something go sideways on their part, you have options to bring them to court or something.
And there're several of these companies, like 3 or more. All with proper audits and everything.
Nobody use paypal or stripe or some similar BS here, also we can send money directly from personal bank account to company bank-account, with no fee, so this is just another option. Or even all banks integrate with eshop in a way, you can make a direct payment through bank API with callback, so order is instantly payed. Also no fee, of course.
I can't comprehend, why is American online market so backwards.