It's kind of funny. I recall watching the recent Apple developer conference live on Youtube and the comments section had been turned off. What are these giant tech companies afraid of?
I would disable them as well, not because of 'being afraid of anything' but because it's a net loss to have them enabled, and nothing of value is lost if they are disabled.
Though, after any ordinary live stream has ended the chats usually are retained as chat history or comments if you will.