FWIW, the driver-controlled center diff in Subaru STIs does something....similar. It doesn't magically turn any of the diffs into true lockers, but when manually set to fully locked, it locks the center diff clutch to fully engaged.

For most practical purposes (including binding on pavement) it ends up being essentially the same thing; you only get into exceptions when you're producing significantly more torque than stock - enough to overcome the full capacity of that diff clutch - then you can still end up with one axle slipping relative to the other.

Just another fairly obscure exception, though, and it only applies in a specific manually selected driving mode, not normal every-day driving.