Cousins has consistently said he is content in playing for the franchise tag and has no real interest in a long term deal. This is just about money, not really about wanting to be with the Skins or not. With two years of franchise tag he will have made $44m guaranteed, and still will have the option of signing long term next year, assuming he does not blow up his career or suffer a major injury. He is taking some chance here, but also getting paid a ton, well above his real value IMO. He would give the Skins a shot at signing him next year when he will be after the long term deal, but he will ultimately be a free agent. From the Skins perspective, they have their doubts if he is the long term answer and probably do not really want to pay him $24m this year with so many holes to fill, and no guarantee beyond this year.
For what it is worth, many Washington fans, and some in the organization, are not sold on Cousins. He has his moments, but he is certainly not elite.