Don't forget BA is first and foremost a business, whose principal aim is to maximise profit- BA feel they can do this most effectively from London. Yes, you may be right that BA could make a profit from flying from Edinburgh to New York (or whatever other prestige route you think), but they have decided that it is a better use of resources to concentrate on a single hub- And yes, other airlines are flying from Scotland, but BA would be entirely reliant on O&D traffic.
BA may lose a lot of passengers from the regions to other companies, but there is simply no obligation for them to fly from what are seemingly low yielding routes from the regions- they are not a government owned company. There is no doubt a reason that BA has been one of Europe's better performing legacy carriers in the last few years.