I'd have thought that it's obvious that sysread blocks if there's no data, but otherwise returns the number of bytes actually read.

Why is that obvious? It isn't mentioned under sysread, or select or in thePOD of IO::Select.

Are all those problems documented somewhere?

Depends what you call 'documented'?

Not that I'm aware of in the Perl documentation beyond perhaps some oblique comments regarding 'legacy' or 'dosish' systems.

The first discussion here at PM that I am aware of, and the basis of whatever I have discovered is Non blocking socket open. For a more complete list of the posts that mention the problems you could try google

Are there any modules which mitigate that situation?

None that I am aware of.

If so, is there any reason why IO::Select, IO::Handle, etc can't be told to use them?

See (tye)Re: Non blocking socket open