Well whether Billund Paris is viable or not is entirely up to Sun Air to decide. They are an independent carrier who PAY BA a % of their revenues to "licence" the BA livery, uniforms, branding etc. From BA perspective the principal concern is that Sun Air does nothing to damage the master brand. Secondary concern is whether there is sufficient traffic /network benefit to justfy the risk. Otherwise it costs BA nothing but they earn relatively eay money. The KEY question is, do Sun Air consider the arrangement worth paying BA a % of their revenues. And clearly for now they do.

I am sure if BA could have franchised the "regions" it would have, but if the regional business was not profitable enough (or at all) then when you add a 10% revenue franchise fee you make it wholly unviable so there would be no takers. (also a secondary issue with the regions was the inability of BA to manage it network reasonably to schedule, working aircraft as hard as possible to try to make a return but on some day crippling the whole timetable when something went wrong.....this borad used to be full of people moaning about very late elays to flights and actually reputaional damage ws being done to the brand, so even if there had been a volunter to be a UK franchise, BA probably still wouldnt want their "brand" geting that bad PR still).

As for the second point you make, Sun Air service being "wonderful" is anecdotal third party gossip/rumour/speculation. But that aside what you can do in a 30 seat plane on a largely short hop network on thin routes with limited competition does not necessarily work on a mainline european netwrk with much more competition