All of that is describable, and many vendors have such products. There are no standards (or none that are significantly followed) for such assertions. So? Many different PKIs can handle such assertions, once you codify them.
Are you saying we need many different PKIs for all the different purposes?
Then, I'm afraid they are PK structures, but not an infrastructure.
OTOH, the Internet is an infrastructure useful for many different purposes.
Masataka Ohta