That seems like it would be a really risky move for Washington. They have no intention of keeping Cousins and franchising him would lock up $34.5 million in cap room not to mention the $17 million they are spending on Cousins. You might get a team like Cleveland, who is desperate enough to offer a trade, but if Cousins threatens to not sign a long term deal, then that kills his value on the trade market. Unless some team is willing to make a stupid deal, then Washington is better off with the cap space and recouping a compensation pick in 2019.
We're already short on draft picks as it is and while Cousins is arguably the best option out there, he's certainly not the only option.