Wouldn't that defeat the purpose of having an arena?
Pretty much.
I'm not a big fan of having to travel across a map to an arena to pvp or clan war. Things tend to lose momentum that way. People get lost, its a hassle to get everyone there and organized, and the arena environment gets old quick. If pvp is out in the open it makes the game more dynamic and exciting. Its also more realistic (as much as pixels can be) in that battles aren't fought inside of an arena, but out in the open environment over very real things like territory and so on.
To me arena fights don't mean anything. You win, you lose, big deal. If clan territories are introduced it would give clans a tangible reason to slash each others guts out.