Just through the sheer repetition of Kirk being forced to literally fight for his survival, this is either one too many or perhaps the tipping point in making it a legitimate trope in the series (and franchise, as in Voyager's "The Fight" and "Tsunkatse" and Deep Space Nine's "In Purgatory's Shadow"/"By Inferno's Light").
Anyway, "Bread and Circuses" also continues the gimmick of doing every story type in existence, this time the Roman Empire, just because.
|via Star Trek|
An oblique reference to Christianity, extremely rare in any Star Trek incarnation, may be the one notable element of the episode. Until DS9 faith and/or religion never got much positive press, as it were, in the franchise. That was a decision Gene Roddenberry made about humanity's future. (Now if this had been the whole point of the episode, we'd be having a different discussion. Incidentally, original Pike actor and series lead Jeffrey Hunter played Jesus in King of Kings.)
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four quarter analysis