Technically possible, but not that practical. It would be harder to keep on-board drivers up to date than having the operating system handle it.
Think of the issues and potential risks surrounding updating your motherboard's BIOS. Outside of the overclocking / benchmarking community, most people tend to only update their BIOS if they really have to - if they need support for a newer cpu, or a major bug fix. I don't think many people would want this for their GPU, sound card and so on.
Also, it's not that practical for the manufacturers. The cards they make could be used in a Windows PC (many different versions), Linux PC (many different versions) and possibly Mac too (many different versions). That's a lot of operating system support to hardwire in. Much better to let all those different operating systems have drivers you install as needed (or as is increasingly the case, native drivers).