Did the rebels need the capitol?

I've been thinking about the Capitol's role in the rebellion, and I don't fully understand why the rebels needed to take it over. In the first rebellion, they went through the Rocky Mountains to attack from behind. In the second rebellion, it was clear the plan was to seize the Capitol. But was that necessary?

The Capitol didn’t supply anything essential to the districts—just security and order. What if the rebels had simply cut the Capitol off instead of storming it? The Capitol relies entirely on the districts for food, clothing, and resources. If those supplies were stopped, wouldn’t the Capitol have surrendered quickly on its own? They’d have no way to sustain themselves without district support.

By avoiding a direct assault, the rebels could have saved countless lives and still forced a surrender. Why fight to take over a city that produces nothing of value? What are your thoughts? Could the rebellion have succeeded just by isolating the Capitol instead of engaging in a costly battle?