This is probably because non-British Anglophone nations are much younger than Britain, whereas Britain has a much longer history, leading to the misconception that British accents are somehow "older" than American/Australian/Canadian accents. Ironically, the most recognizable aspects of the modern British accent are fairly recent linguistic innovations (supposedly, the dialect closest to Shakespeare's English is the traditional speech of Martha's Vineyard, and the most phonologically conservative widely-spoken dialect is in fact General Americanthe "Newscaster English" native to Iowa and Nebraska). In any case, you can create a series or film that is commercially viable in the USA while maintaining the appearance of historical authenticity. Also no doubt inspired by productions of Shakespeare's plays set in Ancient Rome. No doubt if the dominant language of America was French, Gérard Depardieu would be the new Patrick Stewart.
Another explanation involves the fact that English accents tend to be the foreign accents most easily understood by American viewers, and since most major productions are made by and for Americans, and most people speak only one or two languages well, this trope alleviates the need for a subtitled production (which might also cause non-fluent English-speaking actors to poorly affect a foreign tongue) and adds a distinct flavor that's just foreign and exotic enough, while still being comprehensible and thus enjoyable to the standard viewer.
As a bonus, this allows for some subtle characterisation for UK audiences: sometimes, characters will speak with regional British accents that reflect the class or social status of their character by playing up to stereotypes and associations in the collective British psyche
