Something interesting that I've noticed from the various Q episodes is, whenever someone (like Picard) has told Q to go away, within a short period of time he has.
One time he said something like, "I'm leaving because I choose to, not because you told me too."
This does make me wonder if Q has
to go if directly told to do so, whether he wants to or not. If "everyone" were to simultaneously tell Q to go away, he just might cease to exist.
*fingersnap* They're GONE!
The Q continum has the main Q on a leash, it's a long leash but it's there. If he tried to snap a large group out of existence, he'd find himself naked and powerless again.