How would a broadband network help government?

It'll reduce communication expenses.

Large multinational corporations, especially those with business operations that span in several continents have long used VOIP networks to facilitate communication among departments and personnel scattered throughout the world.

A company's internal VOIP network is expensive. No doubt about it. I'm familiar with the equipment and they're pricey. And the broadband internet service needed to make those equipment usable tends to be expensive as well. The last time I checked, a Tier 1 or lease line connection costs in the neighborhood of P30,000 monthly. For an ordinary household, that is indeed expensive. But for a big corporation, that's peanuts, and since such broadband connection is usually unlimited, it becomes a fixed monthy expense. Thus the broadband connection effectively gets cheaper as the volume of communication rises.

The same principle applies for call centers, by the way. They use broadband and VOIP.

The government seems to want the same thing for itself through the national broadband network. And given the size of government, economics of scale will help government reduce significantly its communications expenses. That's how.