While I don't have much issue with the method you use to characterize the nature of Logical lines of Operation... your sequencing of how they emerged and why are a bit askew (I think )...

I'm near certain that logical lines of operation were a part of Army Doctrine (FM 3-0) before our immersion in these population-centric full spectrum operations...

If my memory serves me correctly, not a given, I think they emerged more in response to a shift towards effects-based approach to operations. Not necessarily the system-centric models, but rather the intuitive extension that all combat operations O/D/S are conducted for a purpose linked to a change in the relationship of the friendly force to the enemy, terrain, and civil considerations... as such is often more coherent to establish logical lines of operation with regard to processes/aspects of the environment as opposed to just physical manifestations of the terrain...

To wit, as we wrote the Long-Range Plan for the Stabilization & Reconstruction of Northern Iraq (Mar-Apr 2003), our LLO were Security, Civil Services, etc... with essentially only one oriented on the "enemy" ... all of which pre-dates FM 3-24 or the subsequent re-writes of FM 3-0, 5-0 and 3-07

Live well and row