Server hardware is designed to run in server environments, not home environments. Maybe if you had a basement or something, but the noise on those fans is going to drive you nuts. Off the shelf home desktop hardware is better, but amazingly inconsistent. The NUC platform isn’t a bad way to go if you have the cash.
You're absolutely correct about the noise. Those 1U servers sound like a jet taking off pretty much the entire time they run. However, there's plenty of motherboards that are ATX (or E-ATX), so they fit in regular cases with little to no modifications. (Though, I just keep mine in my attic)
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.
Or drive your family nuts, who will take you with them.
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.