> if a significant amount of film production moves to the UK, it's likely that criticisms of the UK would be more muted.
Have you watched British television or movies sometimes? They're not exactly sparing their country from criticism .. E.g. (the original) House of Cards, Not the Nine O'Clock News, etc.
The other country you mention, China, is a better match. But is that the kind of society that the USA wants to be?