This article [1] on pumped hydro tempered my expectations a lot - It calculates that a nation-scale pumped hydro battery for the USA would need to be about the size of Lake Superior and have a 300 m height drop
Solar and wind while intermittent have so much redundancy they never have week long interruptions. You can look at CAISO's charts of solar output in California. You get a couple of days in the winter where production is off due to weather. But not a week.
The argument that you can't afford 7 days of renewable storage is just restating that the marginal cost of fossil fuel storage is lower than the cost of electric storage. While ignoring the ability to curtail demand.