Ironically the class quests for GLA in the original version of FFXIV (1.0) (of which there were only three), actually did involve the Colosseum and are close to what you want - during the quests the player was required to track down potential new fighters for the Colosseum, and actually got to fight in it against another npc, and it wasn't just a straight 'tank and spank' either, at points in the battle you actually had to stop fighting and do emotes to the crowd to appease them or earn their favour, otherwise you failed the duty. I admit I was very disappointed when I did the GLA class quests in ARR and found not only did I not go anywhere near the Colosseum, I was basically just being used as a 'rent-a-cop'. But I'm not bitter.

Regardless I think the Colosseum could be useful for both 1x1 PvP and a FFVII-style PvE battle arena, as long as it was limited and separate to the main game itself (that is, to participate you physically have to speak to a npc at the Colosseum instead of just going up to someone random in the street and picking a fight with them).