If you really think a 16-18 year old, competitive male, with more testosterone flowing through his body is going to tell a coach he's "sore" or "wants to come out of a game" - you've got to be kidding yourself. While it's your business as a parent to protect your child, going to the coach at HS is tricky. Some coaches will listen others will blow you off and don't want to talk to parents. It's the athlete that needs to have the first level of communication - it's your job to help him with how to handle that discussion.
I think coaches should ask the umpire ;-) - trust me I can tell you when your child has "lost it" or "had enough", but coaches don't pick up on those signs when it's a 2-1 game in the top of the 6th with 1 out... They're thinking 5 more outs that's less than then 16 he's already got. Velo is down, location is sporadic, but they've got their eye on the prize - beside the other guy's in the same boat and "we'll get to him too". All to quickly it's a 5-2 game and now your team is pressing and trying to do too much. There's never been a 3-run HR with no one on base, but the batters sure swing like they can be the first one, but end up dribbling one to the 2B or popping out to 1B. All the while, the bullpen is rested and could have easily got those 5 outs.
While pitch counts are important, I also am of the opinion that there's a mix of pitch count and mechanics that need to be accounted for; however, all too often a coach doesn't want to mess with mechanics because a pitcher throws strikes (somehow) with whatever herky, jerky motion he has. That motion is just not natural and eventually will cause some sort of injury. Imagine being 20 years old and not being able to pick up anything without searing pain shooting through your shoulder... By that time perhaps the HS coach has won his 3rd straight championship banner off the shoulder of the next guy who won't be able to pick up anything.
BTW: TPM while there is snow on our ground 3-5 months out of the year - the indoor pitching instruction business still does well, so many kids are still throwing 12 months out of the year. When we were going through the recruiting process we felt we had to continue with lessons and stuff to be ready for indoor showcases in Jan/Feb even though last game pitch thrown is in late Oct early Nov. Then we were 5-6 weeks away from tryouts - so it's a vicious cycle.