I agree with both of you. You can only pull out what's there, which maybe all of the nutrients but in my mind I would think this would allow you to be almost exact on what nutrients are in the tank because you would have to add them. Say you went with a skimmer 5x or 10x over the volume of your tank. Like a External regal 250 on a 50 gallon tank. I know this isn't very cost effective or practical but just for the sake lets say you have an extra one laying around(Like I do) LOL. This in theory would strip the water clean and you could figure out a dosing system with bacteria and a filter feeder food source to maintain pristine water parameters.
Over thinking all this obviously but not sure if this has ever been something that's been tested. I've always heard over skimming is possible but have never heard any evidence to prove the point.