I suspect that this had something to do with misplaced nostalgia. There is evidence that gladiatorial combats originated as part of Early Kingdom Roman (perhaps even Etruscan) funeral rites. Also, it was part of the Roman mythos that the virile Republican Romans fought their own battles. Of course, by the Late Empire Romans were hiring their fighting done. So having these minature "battles" take place regularly in the city could have been a way to cling to outdated virtues, yet avoid having to risk actual Roman lives.