First off I don't think grid level storage with no backup is economically possible. The amount of storage needed it would be enormous. Assuming the grid is fully solar powered You'd need something like 7 days worth of storage to not have significant length blackouts once every few years.
2nd off, I think Thermal liquid salts storage is the way to go. Some Thermal power plants are already using this method to allow for power production at night. Its extremely efficient, and doesn't require large amounts of exotic resources.
Awe... I did forget PCMs (phase change materials) so many many options :scared:
But... I think the dominate use of PCMs will be in areas where you need heat... not electricity; Like hot water heaters. Add some paraffin wax to a hot water heater formulated to melt at ~120F and BAM! You got yourself a ~3kWh 'thermal battery' with an effectively infinite cycle life for <$50/kWh. To my knowledge liquid salts are limited to thermal solar plants.... which are now expensive compared to Solar PV and it's unlikely we'll see any more being built for many of the same reasons nuclear is in trouble... converting heat into electricity is expensive and inefficient. Thermal storage for electricity is a generally poor option for two big reasons. It has a high self discharge rate (things cool) and it's limited to <50% efficiency by thermodynamics.
Thermal storage may have merits if used as a heat pump... in this function there's less waste heat so the thermal efficiency is much higher. Isentropic PHES is one example of this but I'm I don't think the concept has left the drawing board yet.
I agree that it's unlikely to be economically viable to have enough storage at your home for a week... At least in the conventional sense... but keep in mind that fossil fuels (hydrocarbons) are a type of storage and there are
ways to manufacture those as well. And I'm referring to the grid... not an individual house. IMO we'll likely end up with two types of storage. Short duration (days) high efficiency (~90% round trip) used daily.... what we think of as batteries and pumped hydro. Then long duration (weeks) low efficiency (~50%) with a very low self-discharge. Things we typically don't think of as a 'battery'... hydrogen, un-oxidized metal and synthetic hydrocarbons.
Electricity is likely to be so abundant at some times of the day/year that even if you have to expend 4 units of energy to get 1 unit of stored energy it will still be economically viable. One process I find interesting is
burning metal when solar/wind is scarce then using electricity to restore it when renewables are abundant.
With so many options available the idea that it's not possible store enough energy to carry the grid for a couple weeks does't appear very credible.