It's funny you should bring this up, because I've always said that the "Barney death songs" are the last remaining items in a tradition as old as time itself.
For thousands and thousands of years, every story and every song was simply told and remembered orally, passed down from generation to generation.
Even before the internet, people wrote down the lyrics of songs to archive them, or bands started printing their lyrics on the paper inside the cassettes for everyone to read and memorize.
But kids of the 80s and 90s made up those songs about Barney, passed them down orally, and they are still going strong today. No kid thinks, "Oh, that Barney song that I heard someone singing the other day was funny. I'm going to go look up the lyrics on the internet."
Instead, they ask around to their friends until they get the correct words, then it's instilled in their head forever, and they will pass it down again.
It sounds weird to put so much stock into one little parody song, but it really does represent the last of a dying breed of oral story telling and song sharing.