I agree OP, I just think it's hard to enforce something like that. Like what if players request trades but never officially go on record to avoid voiding their NTC?
NTCs are there to provide stability for players, to demand a trade and then invoke it to control where you go is an abuse of the whole concept of it.
That said I still think that GMs hold most of the cards. GMs are free to attempt to renegotiate the clause with players in these scenarios and, if the current situation is untenable for the player(which it becomes if a trade request is made public), the player might be more motivated to waive it for a destination that was not on his list. If the GM doesn't like any trade being offered by a team on the player's list then tough luck, they need to suck it up and play out the contract or wait until the GM gets a deal that helps the team.