My father has a favorite story from his childhood. His best friend was over eating, and they were having porkchops which was a big deal in my father's house at the time.
There was one extra after everyone had their first, and my grandfather asked aloud if anyone wanted the last, with his fork already poised over the porkchop.
My father's best friend said "Yeah, thanks Mr. XYZ!" and snatched it out from under my grandfather's fork.
Not really contrary to your point, of course. It's a favorite story of my father's specifically because his friend broke the implicit code of "does anyone want this."
> It seems insincere to ask if he didn’t really mean it.
It's not exactly insincerity; cultural nuances like this throw-off outsiders but are not easily apparent to the in-group who have internalized the relevant call-and-responses for the ritual. Consider the standard greeting "How are you?" - the person asking isn't being insincere, but they don't really want to know how you are.
Well, there's also the option to offer to split it. It's not like most food must be consumed as whole units. Asking if anyone else wants it can open the dialog where that option can be presented.
That'd be my default, and I'd be sure to propose it first. I recall eating cheese with a friend. Once it was largely gone, we'd each take half of what remained. We had a sharp knife, and eventually it got very silly. But then, we were stoned.
As I mentioned in my original post, it is somewhat insincere since the expectation is generally that everyone present will let you eat the last porkchop.
With that said, general politeness would mean that if someone did ask for it then you would let them have it, but it happens very rarely in my experience.
I have a hypothesis: perhaps we should interpret "would anyone like the last pork chop?" as "Does anyone need the last pork-chop?".
Scenario A: the Provider offers the last piece to the group. If everyone is sufficiently satisfied and grateful for what they've already eaten, it allows them to express that gratitude and the Provider gets to enjoy being magnanimous; a small-fee to pay for the meal you've just enjoyed!
Scenario B: the Provider offers the last piece to the group, and one who may be in need is allowed to 'save face' by not having to say "I need it, I'm starving!". If this need is genuine (it would likely already be known to the group), the Provider would probably have no problem with this, and it causes the minimum amount of discomfort to the person in need.
Scenario X: You offer the final piece, and some opportunistic vulture swoops in with his fork and says "Thanks bro!". You have now learned to never, ever invite him to eat again.
Edit: offering to split the last chop is slightly beneficial in the short-term (yummy pork), but no one really gets to reap the non-tangible rewards described above to the greatest effect.
There was one extra after everyone had their first, and my grandfather asked aloud if anyone wanted the last, with his fork already poised over the porkchop.
My father's best friend said "Yeah, thanks Mr. XYZ!" and snatched it out from under my grandfather's fork.
Not really contrary to your point, of course. It's a favorite story of my father's specifically because his friend broke the implicit code of "does anyone want this."