It doesn’t have to be an app or a system or anything just call handlers asking a few simple questions to double check, don’t see how this is hard.
In the vast majority of cases, call handlers will be dealing with a stressed / traumatised / injured person, potentially in an unfamiliar (and possibly unsafe) location and they may not be able to accurately describe their location (especially a random road or not of woodland with no real distinguishing features) and W3W adverts have always stated that it’ll get you down to a 3m x 3m grid.
You can understand why the poor person making the phone call is expecting it to be easily understood and can’t get why the call handler is asking for grid ref and postcode and various other checks…
Edit: not sure if ambulance sat nav systems have been updated recently but I know they certainly used to need a postcode, it wouldn’t work off a W3W. Paramedics were often using their own phones as back up.