It would only make sense if it offered an alternative goal or objective to winning.
So far we have capture the flag, conquer and control, zerg, and combinations of them.
We also have open world stuff like a gladiator arena and then actual arenas.
Something that would be interesting to me, although highly controversial, would be a BG where it promotes a more peaceful kind of battle. The objective is to win but without killing the members of the other faction, in fact you would be penalized by it. Instead, each team races towards advancing their base by gathering resources, upgrading technologies and expanding to new locations to diversify their civilization. Ofcourse fighting will be involved if your team wants to steal a location for their expansion or if they are both trying to gather resources from one node, but senseless killing will adversely affect progress, making CC more desirable.
And as far as the resources gathering goes, players will actively need to gather them, unlike the conventional capture a mine and guard it. Maybe even take it further and make it so that players need to know the profession in order to gather.
It would make sense to me especially in an expansion like Legion, where the horde and alliance needs to work together, towards a similar goal, which can be reflected within the bg.