I like the idea of the arena, but needs to be better implemented than in Oblivion. In Oblivion you quite quickly worked up to Champion- the end.
There needs to be a radiant time Arena where you get constant challengers of varying strengths that just keeps going.
I did like the betting thing, that was good. Rooting for the Blue or Yellow side was enjoyable and somewhat creepy...
The Romans had an Arena in every major place (even Britain!) It was entertainment

as well as a message of Roman might-so it makes sense that Skyrim should have one.