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.
The home office's checks there were quietly discontinued a short while after they were rolled out - a short while after the Windrush scandal broke. Regardless, identifying bank accounts possessed by illegal immigrants is probably a use case about as legitimate as anything about controlling immigration is.
(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)
Similar checks are already normal in the EU; national identity card systems, a population registry etc already prevent non-residents from opening bank accounts.
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.
A penniless local citizen who is homeless (thus no residence address) has the right to a basic bank account and no issues with that - all the searches for "open bank account Germany" are obviously intended (just because it's in English and not German) for the special case of immigrants who don't necessarily have a right to live, work and bank there. The above discussion was about unbanked Britons - that's an entirely different discussion, the conditions, arguments and legal issues of poor/marginalized/homeless/addicted/etc people are completely different than the same aspects for immigrants without proper immigration documents, mixing both these groups together makes for a muddied conversation that can't come to any conclusion since what applies to one may be entirely opposite for the other.
