The issue with "base load" is that people usually omit to mention how much GW they are talking about and for how long. Which makes it a bit of a bull shit argument.
As an insurance against unspecified lack (how much for how long?) of wind and solar (and batteries, cable capacity, hydro, etc.) base load is supposed to swoop in and save the day when those temporarily fail locally. So, it's a valid question to ask how much insurance we need against that. Nobody seems to really know. There are loose estimates of course. And people seem to assume it's months and that renewables are going to 100% be offline throughout that very very long period. In reality in most connected energy markets, we have a short gap of a few weeks or so in winter at higher latitudes of reduced output that we already manage to cover with flexible generation.
It's more constructive to think in terms of dispatchable power rather than base load. When the sun doesn't shine or there is no wind, it's nice if you can quickly bring online additional generation, tap into battery reserves, or bring in power from elsewhere (via cables). That favors flexible power, not inflexible power. Nuclear and older coal plants are a bit inflexible. Shutting down and starting up a nuclear plant is really slow and expensive and requires a lot of planning. And especially older coal plants need quite a bit of time to bring their boilers up to temperature such that they build up enough steam pressure to generate power. Until then, they are just blowing smoke out of the chimney. Modern coal plants are a bit better on that front. Same with gas plants.
The modern ones only need about 10-20 minutes or so. Still quite slow but something you can plan to do. Slow here means expensive as well. Because shutting them down when there is a surplus of renewables (which is a very common thing now) is really inconvenient. Which means consumers have to pay extra for perfectly good electricity from renewables to be curtailed. That happens by the GW in some markets and keeps consumer prices higher than they should be because they have to pay for gas/coal that is technically not actually needed.
Batteries have a much lower LCOE than gas or coal plants (never mind nuclear) and it's being produced by the TWH per year now. A lot of markets are serving much of their peak demand using batteries now. Australia and China are good examples. Even in the US, you see batteries being deployed at a large scale now. That's starting to push gas and coal out of the market. A gas peaker plant that rarely runs is just really expensive.