Most real payment processors (e.g. banks, merchant services companies) “underwrite” a company BEFORE allowing them to process. Underwriting means they look over the business model, financials, etc and make sure the business is an acceptable risk, not doing anything illegal or against their terms, etc. So you’re more likely to be declined initially, but if you’re lit up, you should be good for the future because the underwriters actually saw the deal and approved it.
While I haven’t worked for these other companies, a lot of experience seems to show that Stripe, Square and PayPal operate differently: they light up ANYONE, and then only underwrite when the account hits a critical threshold of revenue. So it’s easy to get an account there, but if you scale up, that’s when you’ll be scrutinized and potentially terminated. It’s a very unethical practice because it ends up hitting businesses at the worst possible time, when the termination or suspension causes a huge financial hit.
So basically, always have a backup processor and use these web based services at small scale to prove out your model, but NEVER rely on them as your sole payment solution.