The biggest thing is that all the Muppets on Sesame Street canonically exist in the same world as us at the same speed as us. One week for us is one week for them. If Big Bird died in real life, he would also die in the show. Which would be a problem, since at the time he was the de facto audience insert and was as popular as Elmo is now. It would also definitely cause tone issues which patents might not like. Imagine if Elmo died and Big Bird had to try to explain to Zoe that her best friend wasnt coming back. Or imagine her bringing Rocco to the funeral.