Not the op, but I don't have enough evidence to either agree or disagree with your idea, and I would like to see some evidence either way before policies are set. Lots of things that seem intuitive turn out the opposite way when research is done.

Even defining "illegal terrorist violence" globally is tricky. What is illegal in one country often isn't in another. One person's illegal terrorism is another's rebellion against corrupt government.

"Supressing such narratives" can easily become censoring anyone who disagrees with those in power and until I see evidence that such suppression is actually effective, and that safeguards are in place to prevent it going to far, I'll always err on the side of freedoms over censorship.