Sandia Cooler – Spin the heatsink, skip the fan (youtube.com)

This seems like really interesting technology; where is it now?

If it was a real thing, I imagine places that run big data centers would chase any operational efficiency available.

https://www.frostytech.com/articles/2722/index.html answers the obvious question of "can I run it sideways" (yes).

So why can't I buy one?

Because the impeller spins, heat transfer between the base of the heatsink and the impeller relies on jumping the air gap between them. Which means the impeller isn't actually doing anything and a heatsink with no fan and more surface area would work better.