The mainboard could be a Raspberry Pi class system but with an on-board SATA. There are a number of those on the market. The board would be smaller than the drive.
Seagate should sell such a machine capable of running arbitrary Linux distributions as a kind of mini-NAS.
Oh you mean a home solution for few people who do not require 99.99% uptime, then yeah one could try to go that way although all such attempts I've seen (such as [1]) seem way too cumbersome, I would just build a silent PC, way simpler, more extensible and easily replaceable components. I thought you meant to use RAIN for business servers.
Seagate should sell such a machine capable of running arbitrary Linux distributions as a kind of mini-NAS.