Canada

The property (land) value already calculates the desirability of the area and the specifics of that property (things like views, water access, access to schools, rec centers, etc) in much finer detail than a per-area calculation would do.

Yeah, too finely. If you tax everything, you tax nothing. If people using too much space is your issue you should tax the space.

You really shouldn't make a distinction between the suburbs and the exurbs; it's only a matter of degree. Farmers are a different thing, which is why you'd want to make some kind of rule for "lived-in" area vs. area for other uses on the same property. I know families that live in tinyhouses in the middle of a field, and I know of "farms" that are pretty much leisure space for rich guys who may or may not even live in the area.