one trick for this is to insist that all new cables are installed underneath old cables. Now when that old thick ethernet cable needs to be pulled out it's probably the one on top. If you install new cables on the top then all of he old stuff is buried, and can't be removed because some doofus (who is probably now your boss) will have tie-wrapped it to the trays.
My other thought is that any cables that are unplugged get red-tagged for removal: 5S and the Red Tag Strategy | 5S Red Tags
How you use that is up to you: you could have it that the engineers red-tag cables that can be removed and you get your intern/PFY (google for the reference) to pull out the cables in the copius free time, or wait until you have a critical mass, and have a cable-removing day (especially good if you have a false floor because you can put tape across the doors to prevent accidents and pull up lots of floor tiles at once without having some doofus fall in the hole)
When removing cables, fine anyone $1 per tie-wrap found in the data center.
