Jorge,
Your explanation here does not accurately depict trademark law, to the detriment of trademark owners and consumers alike. I don't have the time to critique every sentence, but here are a few points.
It is highly unlikely that there would be even a few "Lucerne Foods" in a given country; more likely there would be only one. Trademark registrations are, at the least, national in nature (not merely "local"), and a trademark registration for Lucerne Foods (or for "Lucerne" for food products) would almost certainly prevent any other entity from using or registering that mark in that country. "Common-law" (unregistered) trademarks may be more limited geographically, but under US law, a trademark registration confers "nationwide constructive use" on its owner.
Also, as explained before, while a trademark registration is issued for a specific classes of goods and services (or subsets of those classes), the rights prevent use of the same or similar mark for the listed goods and services and any "related" goods and services. Your explanation also ignores the fact that many brandowners have registrations in multiple classes and in multiple countries. It's not uncommon for a trademark to be registered in 60, 70 or even many more countries. Similarly, it's not uncommon for a brandowner to have registrations in 5 or 10 (or even 15-20 or more) of the 45 classes of goods and services. I understand why you want to minimize trademark rights in this discussion, but your depiction is not accurate.
I don't think "rarity" is necessarily germane here, and you confer "rarity" based on a flawed premise. But if we do think there's something to be said for "rarity," there will be many times this benefits brandowners or other potential TLD applicants, and not the entity claiming the geographic term.
Luzern is free to apply for the TLD Luzern, and for the TLD Lucerne. But it does not get global monopoly rights.
Also, I think your interpretation of the "applicable law" provision of the ICANN Bylaws is significantly incorrect. It does not mean that ICANN must simultaneously comply with every local law in the world. That may be a pleasing interpretation for you in the present circumstance, but I can very quickly think of many unintended consequences when applied in any other context, or even this one.
Best regards,
Greg