I can see where pitching Thompson on Saturday would have benefits and drawbacks. The benefit would be if we win one of the first two and the others both lose the first two. Then we are guaranteed a spot and don't need to pitch Thompson and he can go in game 1 of Hoover.
The drawback is that we may lose both the first two games and we have to have a win, or cannot risk the others getting one win, and so we have to have him pitch Saturday. So, he likely won't be available to pitch again for us until probably Thursday, and we likely don't make it that far. If we need to win the series, then pitching him on Saturday isn't as helpful.