That's not doing what's best for the Jets. If Trouba refuses to play for them under any circumstances it would be advantageous to the Jets to trade him for almost anything. Obviously the offers will end up being good because there is a lot of competition. Letting him hold out just spites yourself. You lose one of your best players and get nothing back which is much more harmful than having Trouba improve another team - possibly not even in the Jets division - while also improving the Jets (relative to no Trouba).
There's value in not setting a bad precedent. Trouba is not the last good RFA they'll have to negotiate with. Obviously, you'd rather not be in the situation where a bad precedent could even be set, but they are where they are. For the sake of their future, they can't afford to let him dictate where he goes or overpay him. Nor do I think they have to.
If the trade offers are lackluster, it makes sense to let him rot. However, I don't think it'll come to that because Trouba has a lot more to lose. If he sits until the end of November, he's out 1-2 million. If he loses the year, his development and his career are off the rails. If the Jets don't blink and no one is offering a good trade, Trouba will be begging for any contract at all come late November. At that point, with a team-friendly deal locked up, they'll have an easier time trading him. I expect that'll happen even sooner than November of course - if Trouba really wants out, he'll have to take a bit less money to make trading him easier.