Removing lactate does absolutely nothing at all since it would be removed... and lactate does not contribute to either DOMS or acidosis anyway. So it's pointless.
Removing the inflammation is the only significant thing... which is due to the vasoconstriction of the muscles. I'm not sure if there are any other residual benefits there though -- may look it up a bit later.
Basically, the continuum of "damage" you get goes from regular exercise -> injury and exercise -> rhabdo. With injuries ICE definitely helps significantly.. and this is because it helps limit the swelling and inflammation. Now, to my knowledge I haven't see anything on the lines of it helping rhabdo, so in the context of the muscles themselves it may not help them at all (besides the limit inflammation = somewhat faster healing or limiting DOMS). This is probably something worth investigating.
As far as the Poliquin article.. there's tons of studies on the subject that BOTH ways. Basically, IMO it comes down to black boxing it. I've found it has helped me, so I am going to continue to do it.