Citibank has a similar program in the USA with American Airlines. They issue an Amex-network card and a VISA which are billed together. I think part of the appeal to VS is that BA cannot match this feature because BA's UK affinity card is issued by American Express which is not able to issue cards on any other network.
I also think many excuses for not having a card was because it is an AMEX. Some people dont like or understand AMEX. My family seem to manage it very well.