Despite the migration of many players into the armed services during World War II, President Roosevelt insisted that major-league baseball was too valuable to the fabric of American life to be shut down. The results for those who left and stayed on the home front is fully chronicled in The Game Must Go On by John Klima.
Here's an excerpt:
“Roosevelt raised a finger. He wanted more baseball night games, which many owners, including [Clark] Griffith [of the Washington Senators], opposed as a money-losing proposition. Roosevelt made it clear that this was not a negotiation. He wanted night baseball because factories would run on twenty-four-hour shifts during the war, so people on the odd hours would have a better chance of catching a ball game (and putting some of their money back into the economy) at night.
“Griffith did not push back against Roosevelt’s wishes. The owner wasn’t a fan of night baseball because the electricity was costly and the lights so dim that he thought hitters couldn’t see the ball well. But Griffith agreed and told the president that baseball would ration all essential materials in accordance with the War Production Offices. Wood would be rationed so much that the Louisville Slugger Company stopped making bats and started making M1 rifle stocks. The rubber core used in baseballs could be replaced with something cheaper. Teams wouldn’t produce scorecards because of the paper shortage and baseball cards wouldn’t be printed.”