This thinking was set in place in youth baseball about 8 years ago now. Was going to hit the HS level and did in some states a couple years ago. They are trying to minimize overuse and therefore TJ surgery. TJ numbers have skyrocketed and the powers to be have determined the best way to trim those numbers is through pitch limits.
Pitch count limits are more accurate for stress counts on an arm. A pitcher that gets 30 outs and is able to do that in 100 pitches has a lot less wear and tear on his arm than a pitcher that struggled to get outs and pitched 175 pitches to get those same outs.
Unless different than Little League, Babe Ruth/Ripken and Pony leagues, you should not have to be pulling a pitcher in the middle of the count. In youth baseball the "official" count is the starting pitch of the last batter. So if you start a new batter at 74 pitches, you are allowed to finish that batter with an out or a hit no matter how many pitches it took and you would still be under the 3 day rest category. I would be surprised if that is different at the HS level.