There is no way to objectively state whether a class is good or bad. White room analysis is always going to be flawed based on assumptions, what is being measured and variations in actual play. So we can only determine if a class meets it's goal, which in the case of a game like D&D means that we have to base the judgement on completely subjective measurement, do people want to play the class.
The answer for fighters? It's the most popular class there is. People choose it over other classes because in their subjective opinion it's the class they want to play. Nobody is being forced to play a fighter. So yes, for this particular scenario popularity is a good measure of does the class meet the goals of class design for the game being played. Is it the best possible version of fighter for everyone? That's not possible, it's a compromise like all other classes.
P.S. insisting that something is a fallacy does not make it so. If there is a flaw to my logic go ahead. But saying "People don't really want to play" has no basis, saying "Popularity fallacy" is also meaningless on it's own.
The real measure isn't (or at least shouldn't be) do people want to play fighters - we KNOW fighters are popular and people like the archetype. Many/most people will come at this from a new perspective and pick the fighter BECAUSE it's popular/familiar(movies, books etc.)
The real question is after having played a fighter were people happy with it? Would they play a fighter again? Did they have any of the issues discussed?