This is not an argument for crypto, it's an argument for better regulations so that processors don't make up their own rules.
Better (which I assume is your euphemism for "more") regulation isn't neceesarily the answer, or even particularly the answer. Do you want to force payment processors to do work they don't want to do? Isn't there a word for that?
PayPal is the prime example where it's operating very similar to a bank. You have an account with a balance and can send and receive money, but it doesn't see itself as a bank and in many countries doesn't have a bank license. At least in part this is done to avoid the regulatory work that comes with it.
I absolutely want to force payment processors to do work they don't want to do. For example, banks in Germany are forced to provide you with a basic bank account regardless whether they want to or not. That's because a bank account is simply a must have to take part in modern life. If PayPal decides it doesn't want to do business with you, for whatever arbitrary reason, you are effectively locked out of a lot of online stores that only accept PayPal as a payment method. There is plenty of examples of PayPals really sketchy behaviour online. Every few months you can even see complaints on HN about it.
We might be talking at cross purposes; I'm not sure! How is it like a bank?
If I pay with a credit card, there are processes in place to deal with fraud and charge backs. PayPal is well known to automatically close accounts with little recourse to access the money on those accounts.
They should absolutely be regulated.
But they are nothing like a bank
The feature of a bank is credit creation. Lending more money than they hold.
Unless I missed some news PayPal does not do that
Public utility. That’s what payment processors are at this point, and they should be regulated as such.
If you are on a scale like Visa and MasterCard you're not just any private company anymore. Just those 2 companies control well over 75% of the US market alone. Not having access to a debit/credit card today will effectively block you from taking part in many aspects of modern life. It's absolutely reasonable to place stipulations on what they can and cannot do.
Regulators love working with large businesses like your card duopoly, I don't think you will see much improvement.