I think you misunderstand "base load". What you are talking about is likely peak load, like the problem of everyone putting on their tea kettles during football pauses. [1] In the UK they went with pumped hydro ~50 years ago to solve this.

https://en.wikipedia.org/wiki/TV_pickup

> The base load[1] (also baseload) is the __minimum__ level of demand on an electrical grid over a span of time

https://en.wikipedia.org/wiki/Base_load

It is a constant value. The rest used to be filled by peaker-plants or hydro. While slowly regulating the inflexible "base load" plants to follow the seasonal cycles.

There is nothing inherent to this definition that it must be slow inflexible plants that provide it. More interesting discussions comes from how do you provide system strength, frequency regulation and so on when you decrease the synchronous components in the grid, because those are actual hard questions.

For example, there is ongoing research in grid-forming inverters. This is what you do if you run your solar-powered home in island mode, and as anyone who has done it knows starting electrical engines sucks. It becomes a much more complex problem with destabilizing factors in continent-scale grids.

https://www.pv-magazine.com/2022/08/29/grid-forming-inverter...