They changed to WWE in May 2002, Stone Cold’s prime was already over by then
I would say bc back then less was known about the industry behind the scenes so it was easier to maintain the kayfabe that it was real, and the image they wanted it to be as conservative and family friendly as possible
At its core though, wrestling has always been what it is - A TV show about a sport
I lost interest in wrestling long before that so my timelines wont be exact.
Whether or not it was easier or not because of lack of media and access, fact is in the public eye it went from legit sport to scripted theatre and you could use that analogy and be correct although the WWF/WWE timeline would be slightly off....When i think of WWF i think of Hogan Andre Sheik Bundy when it was treated as authentic sport....it was always treated as scripted crap since being under WWE.