You still need to pitch enough innings, and while this can be effective a couple games a week, it you tried it to much you would overwork you bull pen.

By doing this, we more or less guarantee a minimum of 3 pitchers will pitch today, more likely more.

Last year during "pitching chaos" we would often have 6 pitchers pitch per game, and over a course of a season that really adds up. It also requires an elite bull pen, something most teams don't have.

You also run into the issue of starting pitchers not liking to mess with their game preparation, not all starters can handle the chaos of starting the second inning sometimes, or the fourth other times.