This whole subject of toughness in baseball is a joke to me. You want tough? Go see the soldiers, men and women, who lost limbs or are simply dealing with PTSD--as are their nearest and dearest--before you talk to me about MLB players being tough. There was a day--especially World War I and World War II (and somewhat in the Korean and Vietnam Wars)--when MLB players actually went to war, but those days are long gone with the all-volunteer (and very capable) armed services we have today.
There is a story, I think a true one, about Ted Williams playing in a game right after World War II, during which he served but only as an instructor pilot. It was maybe 1946. The opposing pitcher was a decorated veteran, maybe with a purple heart, who had seen combat. Anyway, Williams hammered one right up the middle and knocked that pitcher down. After getting to first and calling timeout, he joined the group of people standing around the fallen pitcher because he felt terrible about what had happened. But the pitcher just looked up at him and said, "for chrissake, Williams, can't you just pull the ball?"
What was it Ernie Banks said? "Let's play two." He understood so well what Lou Gehrig meant when he said he was the "luckiest man on the face of the earth." Why? Because he got to play baseball--most years, 154 games (he was the original iron man)--at the highest level and in great ball parks and was paid to do it.
These guys are getting paid a ton of money to play a game many of us simply played for enjoyment (I had one year of Babe Ruth League, 1955, and still remember specific games and plays). They don't need to be tough, just talented.