In defence of the OP, I used to work on n benefits. A lot of our homeless or sofa surfing customers didn't have sufficient ID to open a bank account which meant they were reliant on the voucher system where they could have codes texted to their phones (problematic as they often lost phones or had them stolen), emailed to them, or had to come to the job centre to pick them up. They then had a load of cash on them, even if they only cashed one voucher, it was often £100, which may have made them vulnerable.
The post office accounts we used to open with them are all being closed, so we used to try to work with banks to help vulnerable customers open accounts. Some banks would come in on our staff meetings, tell us they'd accept a proof of benefit letter from us, but then our customers were still getting turned away.
Yes, some homeless people may still have their documents, but IME those who had been on the streets for any length of time, or in and out of prison, often had nothing except maybe a letter from DWP and/or something from probation.
To a previous poster, as I have said, homeless people do have access to benefits. Not having a bank account would not prevent that, it just makes more hassle for the person involved.