The posting requirement is old.
About 20 years ago, we changed the requirement of motorized users to have permission - rather than be posted against.
I think a phone number would be more of an opening to harassment.
But I do have some experience on why it is required.
Several years ago, a property of mine was posted... but not by me. A neighbor did not want his grandchildren to see dead deer. The lack of a name and address allowed the LE involved to realize that it was an illegal posting.
Had I posted it, as I now have some property posted, those wishing to hunt have easy access to contact me. If they wanted to harass me, they could just as easily do so by finding out who owns the land in the method you prescribe.
The CU is not promoted by the town. It was enacted by the residents of NH to protect farming for the most part. The provision requires a certain dollar value of agricultural sale per acre... or ten plus acres in the case that not all crops - timber specifically - is not an annual. Of course, they pay timber taxes, but that is to the county... not town or State.
https://extension.unh.edu/sites/defa...76_Rep1099.pdf
I think that is the latest update. So you can see that a piece of prime farmland easily developed for residential use being valued in tens of thousands of dollars per acre would be assessed at less than five hundred per acre. When multiplied against the tax rate the savings to the landowner is significant.
What was considered ''low quality'' land is now purchased or donated to the municipality with a conservation easement on it. Generally accepted by the populous as measure of protecting their watershed.