They primarily want it shut down because it has enabled citizen journalism that they can't control and that is a threat to status quo. Not because people can sell drugs, do money laundering, organize terrorism or share cp on there, that's just the excuse for it. Like it has been for every outreach against privacy and freedom of information.
Ukraine and palestine have probably been the main motivator for this push against telegram. Like Russians can share it's view of the war to almost a billion eye pairs. Western media and adjacent political power and institutions have awoken to the fact and find it untenable when they can't enforce media and information blockade on people. It's not even about the western population since telegram is much more popular in the third world that it's in the west.