Going from 99% black to 99.999% black turns out not to represent that much more efficiency. It's the difference between absorbing 99 of 100 joules of energy vs 99.999 of 100 joules of energy; unless the rest of your system is effectively 100% efficient, it may not even be a noticeable change. It is very likely that other engineering concerns, not least of which is price, is going to dominate this question.

More likely to find use in something like optics, or cameras, where removing any and all stray light is desirable to reduce noise.

There are a few uses for radiative heat exchangers, so its possible it could also find use there.

I can't say anything specific to this specific black, but the previous blackest black all had degradation problems which made them unsuitable.