For me protesting is not just about the impact on society, but about people who care about a thing coming together. At least from my perspective - participating, not organizing - this is not a time sink, it's an energy and awareness source, and a very real way to demonstrate solidarity, at least to each other. It can also be a source of frustration, sure, but even that I always found insightful in some way. I can't predict what other effects it has on those who don't protest, but the effect it has on me I would consider positive. FWIW :)
The country would need to have at least several million protesters
Sure, but you can rarely get from 0 to millions without an in between.
I was also thinking of police (and sadly also mob) violence. I've seen cops just wait for anyone to give them an excuse, or to get the go ahead without one, more often than not. I've seen people behave like shit towards cops, too (the ACAB school of "thought"). And at least for me seeing and knowing about both was and is really important.
Assuming the demonstration is in some form about about abuse of power and the resistance to it, it has a great likelyhood of being instructive, I think. State power has a face, it tends to show it on demonstrations, and having it turned on you is just a "nice" way to keep on your toes I believe. Cancer doesn't really count in that sense, not that I want to belittle it.
But not just state power has a face, being a self-righteous mob also seems to feel empowering to some, and while it gives me goosebumps (not the good kind), I don't regret having seen that either, sad as it is.
I know this is shitty adverising for protests, and that I am probably doing them wrong. But those are my 2 cents anyway, even if they didn't change anything beyond what happened on that day, they were all worth it to me, the shitty ones and the great ones (like walking through narrow streets in Berlin Kreuzberg after fall of night, singing songs, surrounded by cops in black riot gear, being greeted by people on the balconies above us... that one was kinda scary for me, but also perfectly peaceful, surreal and inspiring).
The country would need to have at least several million protesters
Sure, but you can rarely get from 0 to millions without an in between.