Yankee Stadium in its current state is not the same place where Babe Ruth, Lou Gehrig and Mickey Mantle played. The stadium was remodeled in 1974.
Before that time there was no Monument Park because the monuments were on the field. Home plate was moved 20 feet forward and the outfield walls were moved in. The stadium looked nothing like it had in the past, and many people had the same reactions that fans now have about the stadium changing.
The fans are the ones who keep tradition, even though the team will be at another park across the street. Also, George Steinbrenner, not Hank Steinbrenner, has been fighting for a new stadium since the 1980s. As much as you don't like some of the things Hank says, he had nothing to do with the building of the new stadium - it was all George.