The computer didn't identify Wes. Riker and Worf did. All the sensors said was that there was a heat signature in the Jeffries tube. I think you're assuming the computer and sensors are capable of making distinctions that it really can't make.
The computer has been shown to be rather literal and not necessarily rational in a human sense. I don't think your plan to have the computer track bio signs rather than combadges is feasible, because we don't really know what bio signs the computer can pick up.
On board a ship, there may very well be an extensive network of cameras and microphones that can be used to identify and track people. Yet the computer is easily fooled, too. Data mimicked Picard's voice in "Brothers", successfully hijacking the ship. A simple visual inspection of the speaker would've made that more difficult, if not impossible. So can we assume the computer is capable of monitoring and identifying people on its own? It doesn't appear to be able to do so.
Basically, you're assuming the computer doesn't need to use the combadges to track people, but could use bio signs just as easily. Events depicted in Trek demonstrate that that isn't the case. Apparently without the combadges the computer just isn't capable of recognizing people. Even with the combadges active, it can't always tell people apart.
The computers of the 24th century are idiot savants, powerful but naive, not omniscient as you seem to be assuming.