While your points about desktops and the web are spot-on, not all Linux or for that matter Windows computers are used as desktops, not all desktops are used for browsing the web, and not all desktops that are used for web browsing are used for general-purpose web browsing.
A server, a desktop computer that isn't used for browsing the web, or a desktop computer that is only used to browse the web for certain web sites that work okay with ancient browsers can work fine with "ancient" video drivers, provided of course that the machine doesn't have a bad security profile (e.g. closed-source non-maintained video drivers, sigh). Ancient "vga" or other generic-video drivers should be fine under such scenarios, and some of these drivers are open-source and likely still maintained.
Here are some examples of special-purpose PCs you may actually touch in everyday life:
* ATM machines
* Library card catalog or on-site-only-access library database computers
* Touch-screen kiosks in stores or hotels that by design only let you do certain tasks
* Media players running a general-purpose OS like Linux, BSD, or MS-Windows under the hood
* The list goes on
The list above doesn't even count your home media server, the servers at your workplace, your home router, etc. etc., any one of which may run Windows, Linux, or a similar general-purpose operating system behind the scenes.