Intruder alert would benefit from not needing much precision. A lifeformish thing suddenly appears -> intruder alert, regardless of whether the exact or even coarse nature of the thing can be established. A door is forced -> intruder alert, regardless of whether a Klingon, an utterly invisible creature, or nobody enters. One doesn't even need a process of elimination, such as footsteps heard -> is anybody legit present, as per tracking records? -> yes -> no alert. False positives are not a big problem, and false negatives in cases such as the above are covered by other things such as the legit person indeed being there to witness.
Plus, it would explain why starships have security chiefs in the first place. Tracking down all those false positives and/or filing reports in the log would seem to be sufficiently time consuming to justify a department head actually having his own office (as opposed to aimlessly wandering around the ship with a hand phaser, looking for something to do).