I'm not saying it's bad, but it's clearly not a replacement for batteries, given its applicability is quite limited.

The question is about conversion is, is it still cheap if you add a powerplant (i.e. converting heat into electricity) and have to maintain it (moving parts, in contrast to batteries).

As I understand it, this is meant as a supplement to batteries, so that batteries can do most of the intraday load shifting while thermal can store energy over longer durations.

It's explicitly not a replacement for batteries. Did you not read the article?

It's a crucial complement for batteries. Batteries suck for seasonal storage.