If we end up killing any and all public supporting of these extremist views on social media and such, wont we effectively be driving all support underground?
Meaning, we wont be hearing or seeing, OR REPORTING on anything we see that looks like dodgy business, because both the public AND the authorities simply wont have eyes on any of it?
It will all be conducted secretly in basements that friends, family, neighbours, any Joe public or law enforcement will have zero idea about.
Will that actually help us in the long run?
To make an arguably bad comparison.....
If weed is legal, you can spot a minor you know using fake ID in a shop to buy it and let authorities/parents know what's going on.
If weed is outlawed, chances are you're going to see that same kid purchasing or smoking. The supplier will be unreachable and they will happily sell to the minor. It will all be under cover. It will be more difficult to detect and deal with.
I hope I'm getting some kind of point across here lol.
I hear your concerns but I think jihadist terrorism (at least as experienced in Europe) has some unique qualities that thrive on sensationalist publicity and the memetic spread of ideas. ISIS, in particular, needs to have a tight control of the narrative - they can not be perceived as 'losing', no matter how much territory they cede, how much resistance they inspire within their borders and how many losses from casualties and defections they suffer. It's a branding / marketing / positioning operation as much as a military campaign. As long as their brand is successful, they can absorb military losses and still attract funding and recruits from across the globe.
Some of the most successful pushback against radicalisation has been using similar strategies (like deliberately spreading testimonials of disenchanted youths telling they were treated like dirt while fighting in Syria.)
However, that's just a drop in the bucket... ultimately, if you truly want to diminish the enemy's communications strategy, you need to impede their ability to reach their audiences. Censorship and not covering certain news stories obsessively deeply offends our western sense of freedom and fairness but I see no realistic alternative if we want to win long-term. On top of that, foreign powers have weaponized fake news and social media in similar ways and the democracies of the world have yet to formulate a coherent reply to these threats.
As for diminishing the public's willingness to come forward with information/intelligence when you force extremism underground, I don't believe that's a function of publicity - the best quality intelligence is gained at a personal level, requiring community policing and outreach. An outgoing constable, committed social worker or astute teacher will do far more for your intelligence gathering than fear-driven broadcasts ever will.