The Forsaken don't need open authority to exert their influence; they only need to be able to operate unnoticed. A novice is perfect for that; they can go anywhere in the Tower, blame it on orders, and pass virtually unnoticed. Their knowledge of inverted weaves makes them more or less immune to discovery, and they can use saidar on others without being noticed, including Compulsion, Mask of Mirrors (or their own version, I forget what it's called), etc. Not to mention, the BA Hunters will never look within the novices, nor will the current BA who is currently trying to find Mesaana (i.e. Alviarin) ever look amongst novices. A novice makes a perfect disguise.