I think that "burning at the stake" while not historically accurate better conveys the circumstances under which those people were executed because it calls to

I think that "burning at the stake" while not historically accurate better conveys the circumstances under which those people were executed because it calls to mind a "witch hunt" in the metaphorical sense which is a fitting description of the (literal) witch hunts in question. At the end of the day "witch hunts" were a thing of the past and Europe (rightfully) regarded the Puritan's witch hunts in Massachusetts colony the way we would regard hearing about a some practices that we consider barbaric and have long since moved on from. In any case I have edited my original comment to be technically correct.