Is there an example of a real OS for desktops and servers that is secure from this point of view?
I think SeL4 might qualify, but that can only realistically be used for embedded applications, it doesn't have, at this time, many of the features you'd need to build, say, an HTTP API server for it.
I think the absence of real world usable secure alternatives is not really strong evidence, operating systems are like web browsers, there's such huge inertia and network effects in the apps that competition doesn't tend to spring up, "build it and they will come" doesn't work.
On the research side there's lots of stuff. Singularity, the various capability based systems, Qubes (granted more towards the adding-features dimension), etc.
I agree to some extent, but still: if you were starting your own company, would you wait until someone wrote a secure OS? Or would you provide your developers and sales people etc. with an existing OS, and run your servers on an existing OS, and deploy other security tools to mitigate the bugs in those existing OSs?
I think SeL4 might qualify, but that can only realistically be used for embedded applications, it doesn't have, at this time, many of the features you'd need to build, say, an HTTP API server for it.