Parity in baseball - why?

Simple 11.7 and 25%. 

I don't think those apply to high school programs.

....pitching....

In general, it's easier for a poor team to beat a good one in baseball than in other sports, and it's often easier for a single player to have an outsized effect on any given game.

I don't know about the first, but the second is definitely not true. 

You've never seen a single shut-down pitcher on an otherwise mediocre team make the difference in a game?

A random guy off the bench can go 4-4 in a baseball game and make all the difference. How often does the 2nd string RB win a football game?  Or the 8th guy on a basketball team?

As for the first item, the worst teams in an MLB season win ~40% of their games, the worst teams in the NFL and NBA win more like 20%. The worst teams in MLB will beat the best ones every year, often multiple times. How often does the worst team in the NFL or NBA beat the best?

You're offering outliers. That doesn't support the idea of "often."

An elite QB or RB will win a higher percentage of games in a season than a dominating pitcher will. Offensively, in baseball, the contributions of any one player are relatively minimal when looking at the team as a whole.

The elite QB or RB get to do that every game, while the pitcher gets one chance a week.  It's far easier to shut down an elite football player than a pitcher who is dealing.

Son had a kid that went to his high school, went to Wisconsin and now is in the NFL as a running back.  Would dominate lesser opponents, but the smarter teams and coaches would put 9, 10 guys in the box to stop him.  Unfortunately, the QB was only good at giving him the ball.  The RB couldnt run and they would lose.

Same son had a dominating pitcher on his summer team, threw mid 90's, drafted second round.  Other teams could not do anything to stop him, only hope he was off his game, which was rare.  

A pitcher can dictate the outcome of a game more than any other player in team sports.  Except maybe a goalie in the NHL.

“In general, it's easier for a poor team to beat a good one in baseball than in other sports, and it's often easier for a single player to have an outsized effect on any given game.

I don't know about the first, but the second is definitely not true.”

This past season a local county team finished the regular season 6-11 overall. They nabbed the last conference playoff spot.  The program has been a winner through the years. They had a Louisville pitcher commit on the bench with an injury all season.  He gets cleared to play and is ready for the playoffs.

He pitches wins 5 playoff games in a row ( schedule and rain permitted the opportunities) , they just lost yesterday in the state semifinals.  They had to pitch their #2 and lost 3-2 against a team with 17 D-1 recruits. ( that's probably a story in itself 17 out of 23 on the roster, wow)

The run is over but the affect that one player had on that team was a big difference.

  I’ll take a stud pitcher with a mediocre team and take my chances in HS baseball.

It's the hardest game in sports to play consistently.

That's why in MLB the highest payrolls don't always win.