I am guessing the Dodgers don't keep Betts either. Baseball economics are in an odd situation at the moment. Higher payroll teams who expect to be competitive every year are not interested in giving monster contracts to elite position players, but those players are still asking for those contracts because there are still mid market teams willing to hand them out for various reasons.
IF the Nats were to spend on a FA position player, with Eaton coming off contract as well as Sanchez, then . . . oh, there's still no way.