It depends on the country, but in most the police are in charge of identifying persons. I guess thats why the taxdisk ID was a suggestion from the police. Not sure how much easier it would make since, you they can just look in the database for the registered owner.

Not sure what EMT's and paramedics are allowed to do. The medical skills and training varies a lot in countries. From trained volenteers, to nurses to docters. Some can give very advanced procedures on the spot.