> Incidentally, man --help on my machine shows "-k, --apropos equivalent to apropos", which isn't very useful.

That's your hint to execute either 'man apropos' or 'man man'. Both tell you in detail what the flag and utility do.

You seem likely to be very disappointed in the '-h'/'-H' output of utilities from the BSD tradition. The output is often a list of all of the (almost always exclusively short) options presented as a sea of characters... and nothing else.