The same thing still exists in the UK, the banks have to offer a basic account to anybody.
Banks are required to deny bank accounts to people who are disqualified from banking, and also deny them from being added as signatories on shared accounts.
This is why cashless in the UK would be more harmful than in countries where everyone is allowed banking as a right. In the UK, access to banking is a government-controlled privilege, even though most people take it for granted and think that everyone can have it.
https://www.independent.co.uk/news/uk/home-news/home-office-...
Just search "open bank account Germany" or similar, and you'll see you need proof of residence.
The checks tend to be done once by the government, rather than 10 times by 10 private businesses.
(I tend to think the home office is terrible and inhumane and that in general immigration policies are terrible and inhumane, but the above is in the context of those)
Regardless, there is no such thing as people "disqualified from banking". The CMA9 banks (who are required to offer basic bank accounts) have fairly limited leeway to decline accounts to someone (though having defrauded that particular bank is one valid reason why)