Many banks have restrictions that make it hard for immigrants to open an account, even though they're entitled to one by law.
For example, many banks use the same ID verification services, and those don't recognise Indian passports. Others refuse Americans because they're a bureaucratic nightmare to deal with. Others require a registered address which is hard to get without a bank account. Others require a residence permit or even permanent residency. You usually need a bank account before you have either.
Bureaucracy gets messy at the edges.
Bottom line: it's surprisingly easy to become unbanked in EU.
If you move money from a country that threatens europe with nukes. But i see your point. The issue is how can banks separate genuine refugees from people taking advantage of the situation and trying to move illegally acquired money?
There's almost no way just to open account at all, to put some cash there, have a plastic card and use it to buy tickets or pay for Netflix subscription. Moving money is a separate quest, that I can tell from the first hand experience.
I am not saying that banks should have some kind of obligation to open account for everyone. I am just showcasing the importance of cash transactions.