Dinorwig can store ~11GWh and can provide that at 1.8GW (going from 0W to 1.8GW in under 2 minutes) and is ~75% efficient as a store, but it's only got a 6 hour capacity due to the limited size of the upper reservoir.
Something similar built at Itaipu or Three Gorges scale could provide some more serious capacity.
Second, advocating private ownership of electrical infrastructure doesn't equate advocating private creation and ownership of all infrastructure.
I rather like a good straw man; this one isn't.
Sometimes it does.
Many railroads (in the US of A) may have been state chartered and sanctioned, but generally were built and operated by profit-seeking enterprises (such as the Pennsylvania Railroad), negotiating land-sale or lease for right-of-way. The most notable exception is the Transcontinental Railroad, which took an act of Congress to get it started, and another one to end its construction phase. The government didn't build the railroads, they just regulated many of them to death. The (US Federal) government only runs Amtrak, whose primary purpose is intercity passenger, and that's only seen a surge in recent times because air-travel has gotten a bit more onerous.
The early internet protocols may have started as a DARPA project, but the Internet you connect to isn't a single thing, it is a private provider with private packet passing agreements with other private providers. The name resolution system is probably the biggest most visible remnant of government "creation", and one that arguably shouldn't be left with it.
By definition, that means the service will be more expensive than necessary.
What's wrong with the government charging a fee that is just enough to break even year after year?
b) the cost of something (in a competitive market) is determined by supply and demand, not by the amount of profit a supplier makes (or doesn't make).