In the heyday of American protest rallies and marches, they had impact because there hadn’t been much of that kind of thing in the preceding decades, and communications capabilities had come into being in a big way during the quiet years. Martin Luther King’s march on Washington and the big rally & march events of the next decade or so got attention and perhaps frightened the powers that be just a bit, as it wasn’t obvious what all these hundreds of thousands of mobilized citizens might do.
By the time Nixon resigned, though, they were ceasing to attract serious media attention, in the absence of which they increasingly came to resemble a huge herd of sheep pacing around in circles chanting “Four legs good, two legs bad”. (Something I’m always tempted to chant instead of “the People! United! Can never be defeated!” or “What do we want? Xxx right! When do we want it? Now!” or whatever we’re supposed to be chanting)
Actions that were deliberately more disruptive (linking arms and blocking access to a building or closing down a street, entering a building and occupying it as a “sit-in”, or even blocking the exit to a building and trapping people within) have been attempted from time to time to try to get the kind of attention and evoke the sense of seriousness originally associated with mass events, but they’ve been at least as likely to piss off the general public and generate negative public opinion as to inspire and impress people, while evoking a more formidable system response.