Windows comes a wide variety of drivers built in, including a lot of generic ones that match many devices to provide at least basic functionality; for example the display adapter ones that you can't really live with but at least let you see stuff.
In addition to that are Microsoft's online repositories; I'm unsure if there's a single central repository or many; the latter I imagine.
Technically the driver installation doesn't only happen the first time; it happens the first time per port it's connected on. For example, if you switch your device to a different USB port it will need to do the driver installation again. This is a well documented fundamental inner working of Windows (I think?) I can't think of the terminology to use to Google it properly right now; but I think I'm right in saying that it's not an issue you'd encounter on other operating systems that bind drivers directly to the device rather than the port and device that is connected- although I may be wrong.
Regarding your question about identical devices needing drivers reinstalled; I think drivers are bound to devices by a "device id" (it may have a better name than that) which is unique per device; so regardless it still needs a new set of drivers.
Your points are valid that life would be a lot easier if this process was optimised and allowed for persistent re-use of installed drivers; but I am sure there are valid reasons and complications that prevent that from becoming actuality at the flick of a switch.