For a fresh install of my systems I need about 5-6 hours, compiling time included, or a few minutes if I just copy over a backup I have made of a freshly installed and configured system and update it. To me it is totally irrelevant how long it does actually take, I have spare computers that I can use while installing a fresh system, if necessary.
I personally am totally fine to exchange a little bit of install time (and honestly, how often do you reinstall?) for the comfort of having a distro perfectly fitted to my needs.

Well, when I first started, I probably reinstalled a dozen times, because I had absolutely no idea what I was doing.

Now, the only time I have to do an isntall is when I switch distros, and there's not really an option there.

If a fresh install is going to take 5-6 hours there is no way the NSW DET would even consider Linux. If you are a technician doing a government job and installing an OS time is everything. Early last year the NSW DET (Education Department in my state) had all the PCs re-imaged to Windows 7. It took ages to do even small schools with 20 PCs and it took so long that many schools were done during school terms, the job was supposed to be done during holidays. I am hoping to demonstrate to the NSW DET that it can end its reliance on Windows, 1 of the things I will do is show them how quickly and easily Linux can be installed and running for staff and students to get to work. This not only helps the end user but it also helps technicians who have to place a tender for the job.

For all 20 bills?

Guys, I was just remembering the old times, when installing was somewhat complicated and time consuming. 16 MHz 386 SX took around 8 hours to compile the kernel and install the packages from CD. The HW just was that slow.

That is the time I need to do a compilation of my complete OS, includinh heavyweights like Gimp, Blender or Chromium. There are of course ways to decrease that time significantly when needed.
Then I could go with a buildhost setup (one machine produces binary packages for other machines), which significantly shortens the amount of time an install needs, but still offers the complete flexibility of Gentoo. Or use imaging software, or one of the countless other ways to deploy software.
Anyways, we are not talking about enterprise systems here, but

And nowadays? Last time I reinstalled Slacware on my T42 in about 2 hours while drinking my morning coffee before leaving for work.

I've been using Linux (different distros) since about 1996 or 1997 (don't remember exactly).
Although mainly Debian-family distros (Debian, Ubuntu, Mint), Started with RedHat though.
I also run Lucid Puppy for a couple of years on an old machine until the MoBo said "ka-boom". I even changed the processor by-pass capacitors once, but the last one - dead IDE was the sign for me to get a new MoBo.

Anyway, different distros have different ways of doing things and different pieces of SW, like DE, video infra, package system, CD burner, etc. so you always need to learn something new when you change your distro.

In that case, maybe it's not so practical...

Software which replaces software on NSW DET PCs.
Yes you could but that still needs setting up. SkoleLinux can do this and not take a day's work to get going.
When you have different types of PCs in the system it makes sense to have an install USB that can install to all systems instead of having an image for each type of PC.
You are right and I still believe 12 minutes to 1 hour is still much more worthwhile compared to 5-6 hours that you mentioned.

There are two ways to think about this
1. Time is money.
2. Time wasted is time lost doing other, equally valuable, things.

All I need to do is to set up a machine and add the "binhost" flag to Portage's features. Compiling can conveniently be done over night, no human needed in the process.
When I have different types of PCs most likely they will be used for different purposes, which means I need different types of installation anyways. Setting up an image for each type is not more time consuming than creating and testing Kickstart/Preseed files for different purposes.
If you invest the time only once to have a distro perfectly fitted for what it should do then I believe the time is well invested. Also, that an installation needs 5-6 hours (first install of one type of system, after that binary packages can be used) doesn't mean that the admin can't do other things while the machine is compiling and it means that you have a very lean system that is totally in control of the admin and is not dependent on the vision of distro maintainers and does also not really have EOL dates.

In short: There are shortcomings and advantages for both methods of installation, only that the shortcomings for Gentoo over time diminish (once you have a set of packages only updates need to be compiled), so I prefer that method.

All I need to do is dd an iso to a usb, takes a few minutes so I get a cuppa coffee, then do the install.
Two images (i386 and amd64) with a firmware folder for non-free firmware, installation still takes very little time.
I agree totally that is why 2 live installable images dd'ed to a usb works well for me.
That is fine for you Tobi, not everyone wants to get that involved. If Gentoo fits you like a glove that's great but many people don't want to follow the process you do. 12 minute to an hour regardless of your mathematical ability is alot less than 5-6 hours.
I agree there are shortcomings to every method but to make a categorical statement that install times should be irrelevant indicates you are only considering things from your POV and not those of others.

Which is why you don't "install", but build a working system for deployment on multiple workstations.

That's one of the advantages of a GNU/Linux system - you can pretty much switch a hard disk from one system to another and still have a working system (depending on architecture of course).

Well said !

You've never been in a NSW public school have you? You may also notice I mentioned SkoleLinux which does exactly what you said.

True and you wont see an argument from me that says otherwise but you still need to get it onto the drive in the first place.