Once the FG has been hit the yeast realizes its depleted all of the preferred resources such as oxygen, malto dextrose, and some dextrines. The yeast will do its best to keep itself alive by beginning to burn its reserves. By doing this the yeast cells also begin eating diacytal (a chemical created by fermentation which leads to a buttery or butter popcorn flavor in the beer.) As well as acceydamehal which is again a fermentation byproduct which leads to a green apple flavor in the beer. By taking the yeast out of this environment too soon you run the risk of many off flavors, and a very green beer.
This goes for kits as well. Last time I checked the only difference between a kit and a recipe an extract brewer put together himself is the fact that the shop owner has recommended ingredients for you. It's still the same ingredients of extract, hops, and yeast.