Public Land Survey System

Would it be a good idea to add the PLSS (one-mile grid covering most of the U.S.)? There’s data available here: Commercial maps almost always display this grid, since roads follow it, and every land description makes reference to it.
If I were to add this, what would be the appropriate way of tagging?

I don’t think it should be added to OSM, as it doesn’t exist “on the ground”.
This would be better done as a separate layer, which could be shown on top of OSM maps using OpenLayers etc.

There’s some discussion about OSM with a grid overlay here:
(specifically British grid, but its the same idea).

Jurisdictional boundaries don’t exist on the ground either.

Grids are non-existent and are something which should be added during your processing of OSM data, not actually to OSM. Boundaries are real things, whilst not existing physically they do have effects on the physical world.

Furthermore boundaries usually still make sense when re-projected. Grid lines are, however, projection-dependent.

The PLSS grid is used in describing land, and many roads follow the lines because it was easier to build along the edge of a parcel than cut through it. The lines are more visible in the real world than boundaries that change every time a city annexes another property.
It’s also nowhere near a perfect grid, due to the curvature of the earth and the desire to make most squares approximately one square mile. One would not use it as a map projection.