BA aren't under legal obligation to operate any routes. However they are required to use all the slots they have at LHR or lose them. Furthermore, they are severely restricted by bilateral treaties as to which destinations they can operate new or additional services to. To complicate matters even more, they still have to pay the lease costs on the aircraft even if they park them in the desert, so they have to keep utilising to keep cash coming in.

BA can and do pull unprofitable routes, with Zagreb and San Diego amongst those biting the dust in the last cull. The problem is that BAs network is vast compared to Virgins small network, and many BA destinations are already at the maximum service level permitted. Virgin can easily lose a Chicago here or a Toronto there, its only two aircraft to reallocate to JFK. BA would have to reallocate 10, 20, maybe more long haul aircraft if it wanted to pull all the currently unprofitable routes and there isn't enough demand on the network to reallocate all of these.

The reason you can get to the USA cheaper than Edinburgh is nothing to do with Virgin (Branson is a staunch defender of Bermuda II). Its because the US competition is pumped full of billion dollar subsidies which allow them to engage in predatory price wars when they should be bankrupt.