The only situations where Starfleet officers seem to take off their combadges are:
1. Trying to evade sensors due to naughty activities,
2. Trying to evade sensors because malevolent entities have posessed their bodies,
3. There is a high-ranking member of the Klingon High Council who needs murdering, or
4. They need to use it to generate a signal to beam something up or away.
The only situations? What about daily changing of clothes, bathing, sleeping? Do you expect the computer to track Picard while he's sleeping for 8 hours, with his combadge 2.01 meters away on his dresser?
Why not? The computer core is the size of a freaking house, I don't think it's going to have much difficulty keeping track of the locations of its key officers. Hell, for safety sake it should probably monitor their vital signs at all times and sound an alarm in sickbay whenever any of them have a problem.