We do not want a bank specifically for older people. To think that is, surely, to misunderstand this thread.
What I understand the OP to be asking for is which bank in the marketplace best meets the requirements (not needs ), of older people and quite a number of younger people as well.
This is why so many people recommend Nationwide. Nationwide as a deliberate policy of service to ALL its customers has chosen to keep branches open and it is now in the situation where in many cases it is the only bank in town, with all the business advantages that that gives them.
It also means that it suits many older people who are not comfortable using banking facilities on their phone and/or deal mainly in cash.