It's basically a power shift reversal from the first (and most productive) half of a player's career.
Player has zero say in who drafts his rights, and almost no bargaining power until whenever the team decides to offer a contract that buys out some UFA years. The only leverage the players has is to refuse to play...which is really no leverage at all, because he has a finite number of years as an athlete to make money, and wasting them hurts himself more than anyone, thus the majority of the risk falls on them. Teams have basically total control over every player that comes into the league for the best years of their career, and teams can dump said players at any point if they aren't happy with the players having no control over the situation.
Flip to the back half of a player's career, and a select few have enough talent and accomplishments to ask for a full NTC and expect to receive one from somebody on the open market. Not most players. Very, very few. And nobody is forcing any team to give it if they don't want...but they aren't going to be getting those elite players if they don't take that risk (assuming that clause is important to the player).
I have zero sympathy for management here. They have a sweet deal, and they know it. At some point they should be expected to shoulder some risks in a free market setting, and at some point players should actually have most or all of a say in where they play out the twilight of their career.