The Washington Redskins have every right to tag Kirk Cousins and try to trade him. That doesn't negate one fact: it will be difficult to pull off and they could severely damage their cap space, hurting their ability to sign other free agents.
It's a move many have described with one word: risky.
It's not without precedence in Washington. In 2004, the Redskins placed the franchsie tag on cornerback Champ Bailey and traded him to Denver for running back Clinton Portis. It worked because Bailey liked Denver and was agreeable to a long-term deal.