This was demonstrated repeatedly when moot would attempt to delete a problem board like /b/ or /pol/ (diffusing that culture to other boards) or when digg would make a significant change causing an influx of migrants to Reddit.
I doubt they would come here though. If 4chan were to disappear entirely, most users would end up going to 8chan. Voting sites are not compatible with the provocative nature of image board cultures.
>If you lance a cyst, you make a mess for a while, but that doesn't mean you've done much more than expose what was already killing you
Except those users don't just go away. there are infinite places to go, none of which are as big as 4chan. So they find pockets of like-minded users and become even more extreme.
This is what happened after the ban wave of Nov 2014. Many different individuals left /pol/ in disgust en-mass to form splinter boards that cater to their particular ideology on places like 8chan. Spurned users also went to other boards and caused even more problems.
Now instead of a giant shitstorm of unbridled banter from all corners of the political spectrum /pol/ is an alt-right echo chamber like a conservative version of reddit.com/r/politics. Meanwhile there are 10 other echo chambers on 8chan for communists, democrats, libertarians and everything else.
The result has been balkanized echo chambers, worsened extremism and less diversity of ideas, discussion and ideology.
That's a bad thing IMO.
The issue above all seems to be that not that many years ago, most people who got online did so with a computer, and even though that is trivially easy to anyone here any extra step from "I want online" to "I am online" cuts down the chaff. Now people overwhelmingly stab a button on their phone and bang... the world can hear you.
We're truly approaching a horizon past which everyone is online, and "everyone" includes a lot of marginal characters. The holocaust deniers who used to slip flyers into library books now huddle in their hug boxes, occasionally venturing forth to make some ridiculous claim and flip out at the "sheeple" who don't instantly see their brilliance. Tumblr is... proof that the Right has no monopoly on crazy.
I don't think shutting it down has any benefit, but I don't think that keeping it open does either. It just is.