I think this is a good reason not to have subspecies inherit the common name from the species. Duplicate common names have a tendency to confuse those who aren’t as familiar with taxonomy. Even for those that are, duplicates are a recipe for misclicks. So this would create a bunch of situations where the subspecies is falsely getting attributed.
Instead, I think the “a member of…” text should link back to the species (for species that have a common name) rather than to some higher taxon. For example:
could say “Polistes major ssp. major a member of Horse’s Paper Wasp (Polistes major)” instead of linking all the way back to subfamily. There is an open feature request for this to be the case.