I used to believe this, until I realized what the point of left wing political marches are.
It's not about action on that particular day. It's about generating a perception of political consensus.
The left engages in a march...that does nothing.
In the event of a left-wing march, the press cover the event, blow the numbers out of proportion, link the march to other such events, and give the speakers in-depth extended coverage. Politicians then use that coverage as top cover for implementing leftist policies claiming that they have heard the will of the people.
Meanwhile, that coverage has the effect of swaying the average person, most of whom will go along with a crowd.
That part is the most insidious, because as those ideas are picked up, amplified, and consensus is built, it allows the left to subtly outgroup those who stand in opposition to whatever cockamamie policy they wish to implement.