Most people don't use the admin table very often, but I think it is very useful and if I'm done all my tasks it is the first thing I go to.
The admin table doesn't just track where people are, it can tell you if someone vents. For example: if you are venting from Electrical to MedBay, the admin table will show a black crewmate icon teleporting from Electrical to MedBay. So you might want to leave to go towards MedBay and see if anyone is running away from MedBay. I'd say it is a pretty safe move to call an emergency meeting because they wouldn't have vented there if there was somebody in there, therefore it must be them. (Unless they went to kill them.)
The second reason why I find the admin table superior is if you were to kill someone in Reactor, one person in the admin table (the dead person) would disappear, reappear, and disappear again. Making this even more superior to the Vitals, because you know where the body is. So you would go down to Reactor and report the body. (If the body is as far away as Reactor there is a very low chance you would actually find out who killed him though.)
This works on all maps fortunately, but on MiraHQ it is a bit different. Because the only one-way in-out way from Reactor and Laboratory is to go through Decontamination. But if you see someone teleport from Reactor to Balcony, that is impossible. Another thing that makes MiraHQ different is that all vents connect to each other. So it might look like they vent from Laboratory to Decontamination. But they might later teleport to Launchpad. So I would keep watching the Admin Table on MiraHQ, until I'm sure they got out of the vent.