Why? You don't need to provide your National Insurance number when you open a bank account in the UK, or your PPS number when you open a bank account in Ireland. In most normal countries, banks are not umbilically connected to the tax authorities.
If you are not from UK and want to open a bank account in UK you need to provide a TIN. You can't open an account in any AEOI/CRS country without providing a TIN if you are not resident there. The TIN provided within Tax residency self certification form is needed.
Not sure what you are talking about.