The banking industry is very conservative because of regulation. Changing identity over live chat just by answering some security questions seems to be quite vulnerable to fraud.
I can also imagine that changing the customers' address without proof of address could violate KYC/AML rules.
So while I agree that banking in the UK can be a pain (although less than in other countries), I think it's mostly due to legal requirements, not bad intention.
With interest rates that low, retail banking is all about cost cutting. They could save a lot more money if you'd never have to visit a branch, but verifying an identity via chat is not easy.