That is a very interesting take.
Obviously, The Twilight Zone was not shy about using sociopolitical allegories, etc., in the manner viewers would eventually see on TOS, and in general, such episodes were accepted, but i've assumed some had a problem with that kind of story in TOS having continuing characters (and by association, the "world" they represented in Starfleet / the Federation) revealed to have any affinity for "old" Earth history/government, particularly that of the United States.
The "problem" was not the episode, but that group of viewers who watched nearly two full seasons of TOS (up to that point) and missed how various 1701 characters made references to "old" Earth history, traditions and beliefs with a form of respect, if not outright reverence, so the appearance of the Constitution, and Kirk's glowing passion for its meaning should have fit with character traits/perspectives established in earlier episodes.