The big difference is that with a payment processor it's much harder to diversify than, let's say, AWS. If done well, I can quickly switch to another cloud provider without my users even noticing. For payment providers, this is not possible. The user has to at least re-enter their credit card information, which is going to be a big problem for a lot of companies.
But let's say you did it. You finally moved away from Stripe to $literallyDoesntMatter. Now, a few years down the line, $literallyDoesntMatter also bans you, because it turns out, you are still a small business and the new provider also doesn't care about you. Now what do you do?
Serious question: How would you, as a small business, try to diversify your payment provider? Would you go through the effort to support and implement two payment providers and use them roughly equally, so that if one goes down, only 50% of your customers need to migrate? But then you have essentially doubled your risk of getting banned, since you now have two providers that could potentially ban you. What other options are there?