Catchers may make more throws than pitchers but most of their throws are at less than 100% effort whereas all of a pitcher's throws are at 100% effort. However, your point is well taken.
Tournaments make it very difficult to manage workload of pitchers and catchers alike unless you've got a large roster. I don't count throws for my catchers but I do try to avoid having players pitch and catch in the same day. I absolutely avoid that within the same game.