Only baseball begrudges its players protection. Plastic covers for the elbow are called armor. Many think that if a batter is hit by a pitch on the "armor" that the player should not be entitled to first base, unless maybe the batter has had a previous injury to that body part. Does that apply to the head, too? Hitting a player's batting helmet does not warrant the batter being awarded first base unless that player has already had a concussion?
Outfielders used to battle brick walls and other immovable objects in most ball parks. In some cases there was naked chain link fence. Hey, it was cheap. Mickey Mantle broke his foot in June 1963 chasing Brooks Robinson's home run to center in Baltimore and missed three months. I remember being on the subway platform in Flushing Queens waiting for the seven train to take me to high school in Manhattan and seeing the headline on the front page of the Daily News: Mantle Breaks Foot, Out Season.
So eventually padding was introduced. Have you ever touched that stuff? It's hard. Would you let a pole vaulter land on that from twenty feet? The pole vaulter lands on a big soft cushion. You know so that injury is avoided. Since that stuff exists, why not use it in baseball parks? Players would actually be protected. Imagine how cool it would be to see them running into it? Kids would love to play that way.
MLB could also outlaw catches of fly balls that are in the stands. That eliminates players trying to vault onto and over the new stuff. It also separates the players more from the fans on batted balls, hopefully decreasing fan interference.