(1) An OS does not always supply its own drivers. In fact, in the good ol' days it was quite a pain to get certain devices to work properly.
(2) The OS is not primarily responsible for the automated management of driver updates and/or distribution. This is because driver development is not necessarily the obligation of the OS developer. It is the "chief" developer's responsibility -- whomsoever it may be -- to make sure the drivers work with the OS, not the other way around.
(3) The OS tries its best to use the most appropriate driver for a device, but this doesn't mean it will always be the best one. For example, in the early 00's, some of the older drivers for Nvidia GPUs provided better performance than the "current" ones available at the time for slightly older hardware models. The OS developer doles out an automated manager (not always the case) which operates on assumptions made; and, not always do these assumptions lead to the optimal solution.
(4) Drivers aren't always loaded up at boot. I've written various Linux drivers and Kexts and loaded them without restarting the machine.
(5) I brought up (U)EFI because it wasn't stated in the original post of this thread, not because it's "special."
(6) Firmware is developed by the hardware manufacturer or is outsourced to some party to write it for them. OS developers can't do this because they aren't privy to the closed and proprietary knowledge concerning the insides of the device (unless otherwise spoken for). Sure, they could try, but doing so would invariably mean reverse engineering things, and not many companies would be very happy about such undertakings.