There is stuff in all training that we could point out as being irrelevant. Flying is no exception.
A good and intelligent student will always push a teacher. I certainly don't limit my students to what is in the syllabus, if there is a bit of information that I think is relevant, then I will do my best to pass it along.
Much of what I teach did not come from the PPL studies I have done, but from the far greater depth that was needed when I did my ATPL's. My understanding of subjects was far more after completing them than before and my students have benefitted from it.
One thing everyone is over-looking, is the fact that to be an FI you need the CPL groundschool, not the ATPL that all wannabe commercial pilots go through. It is of lower level in some respects as it doesn't cover every subject that the ATPL's do.