Like Fitzovich and Sgt Guinness I agree that's a very interesting & potentially useful tweak to the rules!
My only concern is using it "each turn when the unit activates" (aka: moves?).
Seems to me over the course of a few moves this would completely destroy any cohesion or usefulness the unit might possess… unless you treated the "stragglers" the same way they're treated after a melee is resolved, and automatically allow them to rejoin the rest of their unit at the end of the turn.
Maybe that's the way you meant for it to work all the time.
It could work well, since the unit in question would still have to spend the bulk of that turn understrength, and there would be a danger of the stragglers being hit by a charge, which would probably sweep them away, since they'd always be leaderless and probably count as "shaken" as well.
By letting the stragglers rejoin rest of their unit at end of turn you'd prevent the effect of this new rule from snowballing out of control.
I think it could be a simple & elegant way to introduce a lower level of troop quality to the rules, and I will definitely give it a try the first opportunity that presents itself.
Thanks for posting this, Piper!