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.
Certainly, VISA is much more widely accepted in the UK than Amex, which has a more limited uptake (for example, I can pay my council tax on Visa, but not on Amex). So by going for a provider other than Amex, they are making themselves more attractive.
Since AA cancelled their Visa here, and it reborn as an Amex, I've been stuck without a non-Amex affinity card. All those wasted points and miles
hence the interest (for me) in this one.