Trans-Atlantic
Skipness has presented a well-argued case.
I think he may have overlooked Gatwick's best chance for new trans-atlantic services. If NAS want to operate ex-UK long-haul, they will be able to make serious money operating from Gatwick, especially to NYC.
NAS want to be as low-cost as practical (hence the different ownership and company domicile operating the 787s). That will rule out Heathrow, so they would be serious about making Gatwick work. They are looking for a decent catchment area in terms of population, affluence and propensity to travel, and Gatwick has supported trans-atlantic services before. They will be able to fill their aircraft in single-class configuration at decent yields with no competition.
Any legacy carrier will only join the fight as a spoiler, or as a result of lack of LHR slots. Any US airline not currently operating into London would sensibly choose Gatwick, but would be on the lookout for LHR slots if they became available.
If NAS started such services, on a daily frequency, I think they could 'own' the route quickly, deterring others from competing. They would be operating economical and modern aircraft on a low-cost model, offering good customer service, from an increasingly recognized and respected brand. They wouldn't be comparing LGW-NYC with LHR-NYC, but with other long-haul services on thinner routes. The operation could offer them some serious returns.