Should possessive 's be used when there is no possession in the strict ('this is John's property') sense involved, and / or especially when the 'possessor' is non-sentient?
Achilles tendon [mythical(?)/sentient(?) referent; association not true possession]
travellers cheques [generic sentient referents; association]
the tree's roots [non-sentient referent; non-legal 'possession?']
the programme's cancellation [non-sentient referent; association]
Grammar.ccc.com gives a balanced view as regards non-sentient referents:
Many writers consider it bad form to use apostrophe -s possessives
with pieces of furniture and buildings or inanimate objects in
general. Instead of "the desk's edge" (according to many authorities),
we should write "the edge of the desk" and instead of "the hotel's
windows" we should write "the windows of the hotel." In fact, we would
probably avoid the possessive altogether and use the noun as an
attributive: "the hotel windows." This rule (if, in fact, it is one)
is no longer universally endorsed. [Actually, in certain cases, it sounds more natural to do the opposite.] We would not say "the radio of that
car" instead of "that car's radio" (or the "car radio") and we would
not write "the desire of my heart" instead of "my heart's desire."
Writing "the edge of the ski" would probably be an improvement over
"the ski's edge," however.
For expressions of time and measurement, the possessive is shown with
an apostrophe -s: "one dollar's worth," "two dollars' worth," "a hard
day's night," "two years' experience," "an evening's entertainment,"
and "two weeks' notice" (the title of the Hollywood movie
Notice that judgement calls for reasons of style are endorsed by the article; this is where the true grey areas, the ones worth considering, now lie.
Non-ownership by sentient beings / groups of such has been discussed before (working mens/men's clubs; dogs/dogs' homes; writers/writers' guilds ...).
With dead man's handle, I'd just take the apostrophe as part of the idiom. With nine days wonder, the trend seems generally towards the dropping of the 'associative rather than true possessive' apostrophe-s, but this is not the only practice followed.