Whoever wrote that article is playing fast and loose with the definition of exponential.
Here’s the actual data of global electricity source on a log scale for the past ~15 years
Notice that the line for both wind and solar is inflecting to the right. If it was exponential it would be straight.
The time between each doubling of output is increasing.
It’s close, but not enough to be exponential growth.
It was exponential for a while but it’s slowing down in the last decade or two.
It is, but lead based chemistries tend to wear out and need replacing a lot sooner than lithium ion.
You’re core idea is correct though, there’s a lot of battery techs that are cheaper / better when size and weight are irrelevant.