[Would you rather they wait until the Democrat majority takes over so they can turn it into a show trial? Better to get it over with immediately.]
I don’t think he’s delaying anything. The Senate already agreed to pro for a sessions until 1/19, and the memo just explains that no business could happen before then without unanimous consent under Senate rules, and that also under Senate rules trial begins the day after the impeachment articles are received. It seemed, unless I’m mistaken, that McConnell is proposing changing that rule so it can happen the same day.
But either way, any delay isn’t being caused by McConnell as far as I can tell.
By the way, if I was the President’s lawyer and the impeachment trial proceeds after he has left office, I would advise him to file suit (perhaps for a writ of mandamus or habeas corpus—I’d have to think more about the appropriate remedy) asserting that impeachment of a non-officeholder constitutes an unconstitutional bill of attainder.