In trade school we were told that there was a sequence in accuracy of location. That the wiggler was good to (IIRC) about +- .004, the edge finder to +- .001-.002, and the toolmaker's chair type edgefinder if you needed tenths.
In practice I use the edge finder almost all the time because I'm working to a dimension from some edge. If it's just a layout where I have scribed lines but outside features are irrelevant, the wiggler comes out. I also find I use the centerdrill or spotting drill to pick up layout lines but that's partly laziness. One tool has a 1/2" shank and the other a 3/8" so if it means swapping collets I may avoid it.
There's probably also some historical experience behind what's used. If there is a chuck in a machine that had some wear and runout, just chucking up the centerdrill would leave the point with runout too. The wiggler can at least be brought to the spindle centerline regardless of chuck or spindle runout.