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.
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.