First of all, it's not a question of "refusing to play and demanding a trade." Both parties are mutually seeking a trade. Miami wants to trade him as much as he wants to be traded. Second - if it was the case that Miami wanted to retain a player who was "refusing to play" (which, again, they don't) - as has been said, Ramsey could claim injury and get paid regardless. He has done this before. Teams can file a grievance in such a case, but have virtually no recourse, as injury/illness is difficult to disprove by existing protocols. It's almost assured that if Ramsey remained on the roster, the team would be on the hook for his salary.
Which is undoubtedly a main factor in wanting to trade him. There's no upside whatsoever in keeping him on the roster just to send a message. All you'd be doing is wasting a roster spot and millions of dollars. At least a trade gets you something, even if it's just a late round pick and a little bit of cap relief. Something is still better than nothing, which is what you'd get by retaining him against his will. Less than nothing in fact, since you're actively shooting yourself in the foot by holding him hostage.
As for the premise of this post - I haven't been here long, but I gather that the OP is widely regarded as somewhat of a troll, so I won't give it too much credence. But I will say that I don't think holding off on a trade is problematic. There's no rush to trade him, since draft picks are useless until May 2026. There are no doubt offers on the table for Ramsey, but Grier apparently just thinks he can do better by waiting to see if training camp creates a bigger need for a team at CB. Is this somewhat of a gamble? Probably. Should we take whatever is the best offer on the table right now just to finally rid ourselves of this headache? In my opinion, yes. But I also don't pretend to be smarter than the guys calling the shots, and they obviously have a lot more information than any of us do. So whatever. I'm not gonna lose sleep over it. Worst case, we wind up making a trade in August that's more or less the same as what we could have gotten now, after nobody softens to give us a better deal. Oh well. No harm done.