Yes, indeed. The conversation has started. But what conversation are they having? You seem to think they are talking about the cause being protested.
They aren't.
They're talking about the need for increased police powers to prevent such "anti-social" behavior. They're supporting broad, authoritarian legislation specifically because it includes provisions against the kind of "protests" that make them late to work, late getting home, late picking up their kids from school, late to their doctors appointments.
The net effect of blocking general traffic is increased support for authoritarianism, and greater tolerance for brutality against demonstrators, as we saw from tribal police in Nevada three years ago.
The conversations you want people to be having only come when your protest narrowly targets the people doing the oppressing. When you're intention is nothing more than pissing off their victims, you distract them from taking effective action, not focus their attention.