I am not a cop nor fireman so this is from a military assaulter's perspective.
My A-detachments have 18D Special Forces Medics. When they are assaulters they're assaulters. A B-Team guy may have a full, big-ass med trauma bag on his back but he's an assaulter as well.
I don't want soft or unarmed medics (or anyone else who has to be tended and defended) in amongst my troops while they're taking care of business. We'll patch you as we go but we're there for a specified mission. We'll call you up once we're done. If we're not done and it's not safe to bring you up with full ATLS/ACLS/Trauma suite and gurney we're not ready.
Cool your jets -- if it's not safe to apply aid we're not done. If it's me or one of my guys, yes we want a doc -- but we also don't want to lose our doc.