The union as a whole only cares about the players as a group getting their fair share of overall revenues. Since teams are no longer paying for veteran players in favor of paying younger players, the union must force teams to pay more for younger players.
Quite a few agents have already alluded to this, so I would expect players to demand it.
I doubt owners will give up any control over players, but they may have to change the date players qualify for a full year of survice time. Increasing the minimum salary will already be a pretty big concession on the part of owners.