I should actually give my view on why BA is not openly campaigning for VS demise - because BA may need state assistance in future and it would look bad to the public if they willingly were wishing their competitors to go under.
Back when Flybe was struggling nobody expected things would get so bad that all airlines were at risk and so it was fair enough to say that one loss making airline doesn't deserve special treatment (and when Flybe collapsed Loganair and Eastern started to quickly fill the gaps until covid-19 really took hold).
So I think from a business perspective BA would be happy losing competition with VS and DY. They may have to quit their joint venture with AA at some point which means they'd compete once again with AA but that doesn't mean they leave oneworld and doesn't stop them codesharing on connections. If someone books BA to the US and then connects on an AA flight, it's still better for AA than if someone flies VS to the US and connects with DL. Same if someone flies AA to Europe and then BA onwards.