One interesting thing about going the rack route is that most of the hardware optimizes for considerations a data center/large corporation might have.
That can be nice in a lot of ways (hardware is fairly robust, layouts are usually friendly for quick access/maintenance, overall density of machines is pretty good).
But it means almost no one is paying attention to how much noise these things make, because for most of the target audience that's WAY down the list of things they care about.
I have a couple of - not elderly but not new - 1u and 2u machines, and they are LOUD AS FUCK. I used to run my server farm in my office when it was just spare personal computers (under the table I use for hobby projects), but I quickly ended up moving it down the basement when running the rack machines.
They're just too loud for comfort on a semi-regular basis.
There are fans mods and firmware updates, but in the end it’s probably the best use of one’s time to buy G9+ as they are far quieter. /r/homelab has some great data about these issues.
Also watch out for network gear. A 48 port POE brocade switch was as loud if not louder than the servers.
Pro-tip: if you can spare more rack units, get a bigger server case. 1U is usually far louder than 2+
Otherwise, manual soundproofing is an option, but then you have heat to deal with.
Most servers aren't very loud unless you're stressing the hardware, and fan settings can usually be tweaked, or fans replaced with silent alternatives.
Still, you wouldn't want this kind of equipment humming next to you in the same room, so it's best to dedicate a small server closet, room, or garage, if you have the space.
That said, a custom server build in a rack mounted enclosure is not the same as using enterprise servers. My gaming PC is in a 4U enclosure and is as quiet as any tower PC.
The hot row/cold row stuff makes sense when you've got a data center, but if computers are eating the world then more and more people will need 80u of rackspace total, maybe at 3 branch offices.
The problem is that rack mount plus low noise equals very high cost, if it is even achievable. Eventually I could not stand the noise anymore, and got rid of the rack. So did every single one of my colleagues who tried rackmount.
As others have mentioned rackmount equipment is also expesive, often ridiculously so. I am very happy to leave racks in the data center where they belong.
My second stroke of luck was that the hall closet in my apartment had a corner in it that would exactly fit this rack, telephone wiring junction box was immediately above the rack, and all of the house wiring was straight Cat5 runs from there, so a few new outlet covers and some cable rejigging and we had internet everywhere (but only 2 pair where the phone plugged in), terminated at the rack, which was partly muffled by winter coats. You can't push a lot of BTUs this way, but you can do a few.
My solution before this was to hide a tower PC behind the couch. For the right kind of couch and the right vent holes, you can eat an awful lot of ambient noise by using major furniture. There's lots of space out there for things like this.
I also tried at one point to build an air filter that would fit under a bed (less noise, no floor space, fewer dust bunnies.
I have a 3U setup where the loudest thing in it is the GPU fan on the 1050Ti.
Here is my AIO cooled threadipper in a 4U enclosure
They relocate the noise to where you aren't, so they do address it.
As I mentioned in another comment, my desktop used to be a big Sun server (forgetting model right now) loud as a jet engine. But it was in the rack far from anyone and my desktop was a totally silent SunRay.
I have a friend who keeps his server rack in his unheated detached garage. Works great unless it gets really cold and all the servers shut down due to low input air temperature. Which I never really knew was a thing.
And now that you can get heat pump water heaters, that strategy would work a bit better still.
and the smaller the fan, the more RPMs (noise) needed to move the same quantity of air.