A strongly magnetic wire is rolled into the 4x2,3x2 as the wood goes through the milling/printing rollers. Hopefully a strong magnet material can be sourced that is soft enough to cut. Maybe a isosceles cross-section.
A reel can also be sold that allows builders to hammer lines into be existing frames.
wire is designed so that one pole is always shown at the surface of the wood. Sticky tape with the other pole facing can be used to indicate plumbing, wires and tools that shouldn't be there. The sticky tape would be great for posters.
A sheet rock/Gib with a slight magnetic percentage component would stick to the frame to aid construction. Too much and the frame would become invisible.
negatives: costly for overall gain. pain for electromagnetically sensitive people.
Good for keeping all your magnetic ducks in a row.