No sir. The player wanted the NTC hence he was willing to take less money to get that. The team did not give him the right to demand a trade to only one team. They agreed they wouldn't trade him because he didn't want to be traded. In St Louis case, he was adamant he wanted to retire in Tampa and that's why he asked for a NTC. Team abided because they had no intentions of ever trading him
We are going around in circles so this is my last post and agree to disagree
Yes, I am sure St Louis wanted a NTC because being able to control your future is so valuable. Maybe in fantasy world players want NTC's to give them evidence that teams will not trade them, but that's rather naive. At the end of the day Tampa got him for less money and he got his control of his career.
As for the bold section, are you sure about that? St Louis asked for a trade in 2009 from then GM Brain Lawton, to only one team, New York. There was evidence of this prior to when it actually happened. Both parties sign contracts with the best intentions, but who knows where that business relationship will be in a few years. If teams are willing to negotiate NTC for less money to the players that's their fault in the end.