I agree the NUC is a great platform, but if you could spend less cash and get more bang for your buck, and perhaps have the added benefit of having a platform with ECC memory (not sure if the NUC supports ECC, I'm assuming it doesn't), then I think the latter is what most people would go for (or well, at least what I would go for :p).
We're also talking about home _servers_, so it doesn't seem that odd to me to use actual server hardware. The homelab[0] subreddit has a bunch of folks running actual server hardware for example.
I had plans to build a noise isolated data closet in the basement (tied into the furnace air return) but I never ended up with the right sort of basement.