I had a problem on the Barclaycard website with Visa security password clarification last year. Never a problem anywhere else.
Contacting Barclaycard, and was informed that it was a known problem on some accounts, but they didn't have a time scale for fixing the problem?.
On-line banking and purchases is the way forward, if you can put up with the little obstacles perhaps, and try elsewhere?.
With regards to opening new accounts, this is usually done for confirmation of mailing address purposes. I use a number of these, especially if I pay through PayPal or Google payment services.