If we throw out the idea that the Games were meant to mark a cessation in hostilities, then let’s not go halfway.
Get the SCA in there with their plastic armour and rattan swords and let’s have 1:1 and M:M combat. I want chariot races. I want simulated boarding actions from ‘ships’. I want a new colosseum built every 4 years and events 24/7 to a roaring crowd punctuated only by the sound of pneumatic t-shirt cannons. When they’re done, use them for death-row criminals in actual gear to fight for PPV for victim compensation. MORTAL COMBAAAAAAAT