As you said, it has become commoditised. Is there really a qualitative distinction? Apple's operating supports Apple's hardware (Mac and iPhone). Linux claims great compatibility with most PC hardware and tonnes of other random equipment out there. Windows is Windows. Do you think the average person cares what file system underpins the iPhone or that Android and the Pre share an OS kernel?
But you are right, you can't replace an operating system with browser. However, you can treat the OS as just another layer in the stack in between the network card and the browser. It's even an interchangeable component -- swap out Linux or Windows or OS X and you have still have something that can push bits onto the net and run a browser.
In discussing whether hardware vendors should make their own OSs, if the low level is commoditised enough you don't need to replace it with a browser, you just need to pick the one that better suits you (e.g., Apple with FreeBSD).
As far as the user experience goes, non-Windows systems are still handicapped by hardware and software compatibility issues which are decreasing in relevance, especially for a hardware vendor who can ensure that at least the hardware it ships is fully supported in their OS of choice.
Because it is readily available in free form, it is no longer important, significantly or otherwise? Seriously?
Yes - it's become more commoditised. No, you can't just "replace" it with a browser. And yes, there is a qualitative distinction in degrees of hardware support and underlying engineering.