conditioning

The intensity of post game / practice running is at the discretion of the coach.  It's probably going to vary based upon how hard / easy the coach thinks the preceding game / practice was.  Throw in extra running for effort / discipline reasons, and the amount of running from one day to another can vary greatly.

I don't see why there is any correlation between finishing conditioning and starting a game.  The coach sets the lineup based upon many factors.  Performance in conditioning may or may not be one of them.  It should also be considered that "finishing" conditioning may have nothing to do with the player's effort. There are always going to be other factors that come into play.

Ultimately, if the coach feels not completing conditioning warrants benching a player, then that is his decision to make.  Obviously this is a matter that the coach should have made his rules clear on from the beginning.  Then nobody has to worry about whether what the coach did was "fair" or not. 

Develop drills that get the conditioning done for you so you don't have to set time aside for practice or after games.  For example we used to have a run down drill that would have them dragging their tongues when we were done.  Accomplished two things 1) got them in shape and 2) we got better at executing rundowns.  

Throw in some communication drills for OF in gaps so they are constantly running.  Do some baserunning drills in small groups during BP so they get to work hard.

Once I figured this out (probably someone else told me about it - I'm not that smart to figure it out on my own TBH) practices got so much better and I was able to accomplish so much more because time wasn't being spent running 40's or 60's or poles.

I am not sure where you are going with this one coach. 

Baseball is a game of failure. It is NOT a game of not trying hard enough. If the player is trying, and giving his heart out, but not conditioned yet, then why would you punish him for that? 

Now if he is quitting and can't complete the task and gives up, this is another question. You can still keep trying but not complete a task and that to me is not a problem, giving up is. 

It was my observation that the best HS programs I saw were the ones that separated the fall conditioning from practice. They either did it in the morning or used the "practice time" for conditioning. The very best ones really got into strength and conditioning early as incoming freshmen and continued it through their Sr season. 

I know a lot of college programs have made fall conditioning ingrained in their culture and have a competition, and team building.

Here is just one example:

https://www.youtube.com/watch?v=DAX4DhvJoAY

Good Luck with your team!