Indeed, the board in the video (Radxa Taco, hopefully for sale next month) would actually make a decent 1 Gbps NAS (with a 2nd 2.5G port if you want to also use it as a router or have higher network storage speed for short bursts) for HDDs.
Most of the average NAS HDDs top out at speeds that are within the Pi's performance realm, though software RAID and ZFS both bottleneck a bit, so you can't get a full 2.5 Gbps (2.3 Gbps real-world) through the Pi to the disks.
Interesting, I have an old HP MicroServer laying around gathering dust. It only has a dual core AMD Turion (like Intel Atom) and 4Gb of memory. It should be easy to retrofit this with a Pi, in fact there's an empty 5.25" drive bay on this case.
Most of the average NAS HDDs top out at speeds that are within the Pi's performance realm, though software RAID and ZFS both bottleneck a bit, so you can't get a full 2.5 Gbps (2.3 Gbps real-world) through the Pi to the disks.