I'm pretty sure that ship has sailed. Users (and perhaps more important, companies) do, in fact, want web browsers to do everything. Even traditionally heavyweight applications like Microsoft Office and Adobe Photoshop are shifting to the web.
Whether that's a good idea or not is certainly open to debate, but pretending that it's not happening isn't the answer.
It's more of an abstraction layer over operating systems than an operating system. Crippling APIs (try opening a datagram socket. or send icmp pings). No gpu-compute, no shared-state multithreading.
It doesn't manage hardware or anything like that.
People use browsers as if they were an operating system. That does not make it one.
It's like calling a java virtual machine an operating system.