I just read the news in the energy market. I think California just ordered a few MwH of battery from Tesla. They seem to be doing a brisk business of selling batteries to grid providers in a market that is entirely supply limited. There are loads of companies working on alternate storage technologies.
You are right that there is very little right now. But I'd counter that that is growing rapidly and that that is inspired by those investments paying off for their early adopters.
Short term stabilization is actually the key problem that needs solving with energy peaks (which are inherently short term). The sun comes out quite reliably every day to provide a predictable minimum of power levels. Basically solar and wind combined are quite OK. Things like seasonal variation are actually more predictable and something you can plan for. Extended freak periods of clouds with no wind across an entire continent is not a really thing. Such effects tend to be local and temporary. So we can fix a lot by simply moving power around (with cables, another proven technology).
The unspoken presumption with storage critics is that we'll need unspecified days/weeks/months of storage for such apocalyptic conditions. As far as I can see this is simply wrong and not something that energy companies are putting a lot of serious money on the table for.
I've actually seen zero credible evidence for this; not even a ballpark number of how many TWH of storage that would be needed. So, I'll bounce that question right back at you: how much TWH/PTW do you think is needed/economically justifiable and why? That will allow us to put a price tag on it.
The reality is that interconnected grids means the sun is always shining somewhere and wind turbines out on the water or wherever are always providing some power somewhere. If you look at the market, grid connectivity and storage are exactly two things where investments are happening. Long term storage seems much less of a concern for grid providers. Mostly 2-4 hours seems to be the sweet spot of what grid providers seem to be spending on.