You can bring your own merchant account to any saas e-commerce site and not have to worry about getting your money frozen. Most banks offer merchant accounts and you just pay for a gateway like authorized.net. It’s going to be $30/m gateway and $30/m merchant account + setup fees.
Yeah, that's how I used to do, and it was quite simple. I actually had much much more trouble with things like Recurly (whose API and packages are absolute garbage, IMO) and even Stripe than with the simpler gateways.
The only problems I had were solved with a few phone calls, as I had a bank manager very interested in doing business with the company I was working for.
But I was not in the USA/EU when I did this stuff, so I have no idea if Stripe and co. have improved things or not. For me (I later moved to Europe) it was a massive regression.