This is how I remembered it as well, but someone in another discussion reminded me about conservative talk/TV hosts getting people fired and shows cancelled. Focus on the Family, Glenn Beck, etc all pulled these sorts of campaigns. I wish I had links for you but I can assure you it did happen, if you doubt it then a little research should bring it up.

What has changed, other than the outrage culture mob moving to the left, is that the mob is now empowered by social media to coordinate and move more quickly. This makes them much more powerful than the conservative cancellers were.

Edit: social media also allows anyone to start a cancel campaign, whereas previously you had to be a public figure in order to get any traction.