To run a syndicated show, the station has to give up half of it's advertising inventory to the syndicator. So they may not have to pay the talent, but they make only half of the money during the show. So it costs money to run syndication. Unless you're so poorly rated that you can't sell it anyway. That's not the case with WGN, and it's why they prefer not to run syndication.
I doubt it. They run so little syndication that it seems like a philosophical decision and not a business one. It probably does not make business sense to have a live talk show host at 4am on Sunday morning.
I would add that a few "high demand" syndicated shows require cash in addition to ad inventory. Limbaugh at least used to be an example.