Base load is one of those terms that nuclear power proponents love because it turns a negative in a positive. Nuclear plants are very expensive to turn off and on. Nuclear plants leave you no choice but to leave them running 24x7, even when power that is an order of magnitude cheaper is available most of the time. Proponents call this base load. But technically it's just very expensive power that you can't turn off when it's completely redundant.

Flexible load is where the action is these days because renewables sometimes push energy prices into the negative whenever there's too much of it. Having to expend fuel during such times is a negative thing.

The big benefit gas plants have over coal and nuclear plants is that you can turn them off and on quicker. So you don't have to run them 24x7. Newer coal plants are similarly cheaper to use for backup power generation. A common mistake with assumptions about Chinese coal plants is that yes they build lots of them. And no, they mostly aren't running a lot. Their coal use actually is starting to decline. The new plants are more flexible and they use them to replace the older ones.

Renewables are plenty and cheaper most of the time. Batteries can deal with short term fluctuations and help time shift renewable power to cover peak loads in the morning and evenings.

And if you can bring online some gas/coal power when it's actually needed, there is no need for base load.

In practice this is still quite often but not most of the time and gradually declining. With dirt cheap renewables + batteries coming online by the hundreds of gw per year, the ability to turn the rest off is the most important feature with backup power generation.

Nuclear plants remain stupidly expensive and lack this feature.