Litigation does not speed up the negotiating process. Negotiating speeds up the negotiation process. The players want litigation because they think they can get the best deal that way. Not because it's fair, or because it's efficient, but because that's how they think they can get the best deal. Like the lockout, it's just about creating leverage.
The interesting thing about the litigation strategy, is that if it backfires on the players they will have given the league a whole lot of leverage. Litigation carries risk for everybody involved (except the lawyers.)