I do not agree with this premise because the argument from the players' union is not entirely about "stars" getting to big contracts quickly. It is also about the middle-tier players, like a Brad Miller, and how they've been squeezed out of the market or signing later or having to accept minor-league deals. It's also about dozens of young relievers who are churned through rosters over and over early in their career when their salary is suppressed/controlled and then they're out of the game/taking less/injured before they have a chance at the larger dollars.
That's a major part of this labor clash: the practice of teams to go with the cheaper, younger player earlier instead of the better, older, but costlier pitcher. It's been a trend. Notice how teams turn to 0-3 pitchers -- Class AAAA pitchers in some cases, if you will -- to be long relievers, or middle relievers, and then where do you see those players go once they reach arbitration. Look at the Cardinals' practices with Bowman (Rule 5), Maness, and even this past year Gant. What happened to them as they reached arbitration and started to make money that was more reflective of their contributions ... ?
It's not just the stars that are being brought up by the union as an example of how the market is impacting the earning potential of players. Not at all.