If you fail to get the lock, then you have to wait on the lock, so you might as well go into the kernel anyway. That's the reason futexes do that, instead of just letting the thread spin.

True, there are scenarios when you might prefer to spin, but they're pretty specialized.

My blog post was quite clear that I'm talking about futexes

No, you never mention the word "futex."

When somebody says "mutex", you have to assume they already mean "futex".

I don't think that's a valid generalization at all.