That'd be like making a Call of Duty: 3000 game. Mass Effect 3 had this stort of arena thing tacked onto it, and a many felt the overall game suffered terribly as a result. A lot of development time and resources went into producing a mode for people who simply didn't want to play the actual story part of the Mass Effect series but wanted a generic shooter. The thinking was the game would appeal to both Shooter fans and to RPG fans, the result was a game which was slammed by both because it was very compromised as a result. I think doing that here would result in the same.
It seems to be a modern trend of gaming that all games with any sort of combat in them get a special PvP ultra super death combat mode tacked on (whether online or offline). That's a fun thing, but games that specialize in such things are generally far better at it. Trying to compete with them only creates a sub-par mode.