What might work would be a have a check box on the opening screen before you select the arena that said "Put me where ever I am needed most"
That could cause someone some grief, although I appreciate where you're coming from.
Back when I first became a scum sucking side- switcher I used to switch to the lowest numbered side as soon as I logged in. It didn't take me long to realize that wasn't such a good idea. Sometimes the side with one or zero players on it is limited to a place on the map where nothing is happening.
For instance, Rooks would have 0 on so I'd switch to rooks. Problem was, despite having 0 players, nothing was going on with the Rook side. Knights and Bish might be having a knock down dragout on the other side of the map and there you sit trying to find a fight. It could also be the lowest side is in a bad situation with few bases and those they do have aren't close enough to the action to get something going.
More than once I'd switch to the low side and there I would sit for an hour waiting to switch again. I quickly learned to read the map and roster, check the layout and where the best possibility of a fight was. Not sure an automated system assigning the "needs most help" would be able to avoid that.