The presumption would be that you have an existing Mac to run it on. For a large operation, the cost of buying hardware for this function is 'in the noise.' For a smaller operation that already has an investment in Macs, taking an older Mac, adding an external hard drive (if necessary) and running OS X Server on it for Software Updates is a wise use of existing resources.
As far as lights-out, Server comes with a remote manager that you can run on other machines (although you might have to pay $20 to get it on the machine you want to use to manage the otherwise headless server installations.) So that's not an issue. That being said, Minis do have some annoying issues rebooting when they're "headless". My Mini systems running Server get rebooted only when there's a Mac OS X update, that happens maybe 4 times/year. So screwing with the monitor and keyboard when rebooting the Mini is an acceptable cost for me.
I've been running OS X Server on low-end Minis since "Tiger", for at least 10 years, for file server, web server, internal DNS, LDAP, VPN for my small/home office. Earlier versions of Server were -expensive- (retail $1k!) and hard to configure. Over the years it's become a lot easier to configure (once you get DNS set up exactly right) and of course you can't complain about 2 orders of magnitude price decrease, particularly for what you get.
Now if you have the skill and the patience and the significant user base to justify a pure web-cache solution, go for it! But it's not quite clear to me that solution will understand some nuances on whether the currently cached software update (Mac OS or iOS) will work for all devices on your network.