It is a bit easier with parcels that touch at corners, but that isn’t unique to using a checkerboard. With almost any way you cut land into parcels, people can

It is a bit easier with parcels that touch at corners, but that isn’t unique to using a checkerboard. With almost any way you cut land into parcels, people can surround a plot with land they own. Also, this doesn’t require a single owner to own those black squares. It could also be four individual owners, each building a (virtual or physical) wall on the border of their land. Because of that, I expect that any civilized country has laws that give land owners and their visitors the right to reach their land, so that they can benefit from owning it (https://en.wikipedia.org/wiki/Right_of_way https://en.wikipedia.org/wiki/Right_of_way)