Yeah the community-owned-ness thing makes a ton sense to me as an explanation for why it feels weird: my expectations are completely within the framework of strict secular personal property. If you leave it in the house, it's mine, and it certainly doesn't belong to some movers that you never met. But conceptualizing the Jewish community as something that owns mezuzot (and even kinda owns the house itself in a lingering sort of way after the last family moves out) makes those actions pretty sensible.

Then again, of course if this actually happened to me I would totally be like "oh ok sure have it" since I have no use for a mezuzah.