That method just doesn't work in Manhattan, where due to buildings, you're lucky if your GPS is working, much less the compass to tell you which direction to face.
To correct this you need something like QZSS or accurate models of the buildings to compensate for it.
Even short buildings have issues here - if you walk down a wide street in Tokyo, which are pretty common and often surrounded by 3-4 story buildings, with the map open and look at it closely, you will often show up on the other side of the street. (Which surprised me, because it's literally why QZSS exists.)
Afaik, the issues with WiFi are that if you're traveling at any speed there isn't much time to do scans, and the position of the WiFi networks themselves isn't clear enough because of multipath (reflections), because it is crowdsourced from other devices that don't have real ground truth locations, and because the other devices gathering info are at different heights above ground or are indoors.
The main advantage of A-GPS with WiFi is that it starts up faster and that it mostly works indoors or when you can't see any satellites.
You might be thinking of https://en.wikipedia.org/wiki/Differential_GPS.