This is a very interesting social phenomena and I'm glad someone randomly linked to it since I never heard of it. I imagine the effectiveness of it stood in the fact that cities were self-sufficient. Since cities are no longer self-sufficient, a protest like this in the modern age would be meaningless. All the plebs of New York could leave the city and nothing would change, except that some patrician would get richer…
Rome was highly dependent on grain imports.
> All the plebs of New York could leave the city and nothing would change
All of them?
Transport would break down fairly rapidly, since you'd have no public transport, no cabs, and no Uber drivers. Even if you could get into work there would be nobody to buy lunch from, and no childcare or schooling available to leave your kids with.
Most of the financial services companies in NY would be rendered inoperable.