In general, the Old Nationals fell because the Griffith family had no money except what they made from the team, and from renting Griffith Stadium to George Preston Marshall and the Redskins. Connie Mack had the same trouble with the A's, and Bill Veeck had to sell the Browns to the millionaires from Baltimore. By the early '50s, a team needed an expensive farm system. Later, the great Bill Veeck was forced out of baseball because he could not afford to keep up in free agency.
Leonsis would be a poor-man owner. It looks like his main income is from the Caps and his network.
The Nats would suffer. Looks like a Leonsis-owned Nats would behave like a small-market team. The Old Senators and the Expansion Senators show what that is like.