There's a germ of a good idea in there, but they've got it backwards: Big cities like Chicago need to "secede" from their states, like the free imperial cities of the Holy Roman Empire. "Secede" here being a colloquial metaphor; the real, legalistic action would be declaring Dillon's Rule void, and taking state-like sovereignty for themselves.

It makes sense on many levels: Cities are where lots of people live close together, and their infrastructure, services, public health, and governance needs therefore are very different than rural areas. They are the economic powerhouses of the world, and we need to let the city leaders nurture that power by responding to their local needs. The political polarization divides largely on urban/rural boundaries, and our antiquated political system dilutes city-dwellers' votes and influence.

Lastly, our political system is broken, and can't be fixed entirely within the system. But tearing down the system will definitely lead to chaos. (See: actual secession in 1861.) As I see it, this would be a radical move by the cities, but it would solve a lot of issues in the political system without tearing it down. It's unlikely they'd get representation in Congress the way that free imperial cities had representation at the imperial diet, but even just getting out from under the thumb of state legislatures would be a huge step.