The league just proposed a signing deadline and the MLBPA rejected. But yeah, it could be on the table for the CBA. Obviously the most powerful agent in the game would be against it and the MLBPA answers to powerful agents.
I think it's the owners who have created the current situation though. Teams used to step up and sign their guys immediately. Jim Thome was signed on December 5. Roy Halladay was acquired and signed on December 15. So was Cliff Lee (the second time). It's only because the teams have started valuing the free agent market differently that the players have had to wait longer. An artificial deadline just puts even more power in the hands of owners who aren't willing to spend, by taking away even more leverage from the players.
Would it have been fair if Bryce Harper had been forced to take $50 million less because of he could only get a minor league deal after January 31? He probably wouldn't be on the Phillies either, btw.
Conversely, Lee and Thome signed quickly because the Phillies offered them what was obviously going to be the most money any team was going to offer. They could have done that with Harper or Machado too. They preferred to wait too, and it saved them $.