Completely automatic is obviously silly because of the fraud risk, but a presumption in favour and/or formal restrictions on acceptable criteria for refusal aren't nearly as absurd as you're implying.
We're talking about a very closed industry and a service that, in practice, directly affects people's ability to trade.
We regulate service providers in other essential industries, and they can't deny provision to a customer just because they don't like them. It's part of the deal if you want to operate in those markets.
And there are all kinds of laws to prevent or restrict one-sided deals that inhibit people's ability to trade. There are laws about monopolies and anti-competitive behaviour. The handling of non-compete agreements in employment law would be another obvious example in a slightly different context.
I'm not looking for anything so dramatic, just that merchant account providers should recognise that they are dealing with a separate legal entity. Identifying the key personnel is reasonable, and so is wanting to check them against databases of known fraudsters etc. Asking to see financial statements, business plans, projections, etc. is all reasonable too. So is requiring a cautious degree of funds retention until the trading patterns become clear is reasonable. I really don't have a problem with a merchant account provider wanting to know who they're dealing with and to have some confidence that the company is a viable business; that's only fair.
I'm simply arguing that putting members of the company on the hook personally is not fair. If you're going to have companies at all then you have to protect them against such arrangements by law or you've devalued the entire concept and undone whatever benefits you were hoping to achieve in terms of incentivising entrepreneurial behaviour in your economy.
For the record, I'd add demanding direct control of the company bank account as a red flag as well. Aside from the glaring potential for abuse or error by the merchant account provider (for which, by the way, the company directors will once again take the heat), this has obvious implications if the company ever fails: it allows the payment company to grab whatever it decides it's due before the usual legal mechanisms for dealing with corporate bankcrupty get a look in, for example. And what if there's more than one payment service involved? Do they get to race to see who can empty a company's bank account first if anything does go severely wrong?
IIRC the US has a concept of bankruptcy protection to isolate a company that's in trouble if they have a reasonable plan to extricate themselves rather than failing. Not running a business in the US, I don't know all the details, but it seems a reasonable premise. But what happens if that company has signed over direct access to its bank account to a merchant account provider, who is risk averse and doesn't like the chapter 11 filing?
The bottom line is that these are all worst-case, doomsday scenarios, and even if a company is going to fail, it's usually not going to fail out of the blue and to that extent. I think you're obsessing over a fraud risk at the expense of making it much harder for people to run honest companies. If the system is set up in such a paranoid way, it's hardly going to be surprising if legitimate entrepreneurs are put off starting up, obviously leaving a disprortionate number of fraudulent applicants.