(emphasis in original)
I'm terribly sorry, but this is 100% incorrect. Uniform or no, badge or no, armband or no, patches or no...an EMS provider has absolutely no more legal authority than an ordinary citizen at an emergency scene. Bystanders might listen to you...or they might choose to beat you senseless; you have no control over them. And EMS providers have absolutely no business attempting to render any scene "safe." In fact, it's just the opposite: EMS providers have a duty to stay clear of a scene until it has been rendered safe, by duly sworn and/or commissioned law-enforcement officers.
"Dead heroes save no lives." This was a truism when I first entered EMS some 18 years ago, and it's true now. How true? Ask yourself this: what's the first thing an examiner at an EMT practical exam (in the US, anyway) wants to hear out of your mouth when you're given a scenario, be it trauma assessment, medical assessment, CPR, or any of the other stations? "BSI, scene safety." In NYS it's a critical item; don't say it, you automatically fail the station. That tells me it's just as important as assessing the ABCs. Possibly even more so, since if you enter an unsafe scene, you're dead before you get to the A, and now the other half of your crew has to wait for the scene to be rendered safe before he/she can tend to two victims, instead of just the original one victim that the crew was responded to.
Back on the topic of badges...I think they add an immense amount of class to a Class A uniform. But I have absolutely no reason to wear a Class A uniform with my current employer. And where I work, badges == targets. Bullets don't care what the profession of the person they puncture might be. Nobody in the company carries a badge; in fact, I don't believe anyone in the company owns a badge, at least not in our operational area. And I truly believe that to be a Very Good Thing Indeed™. YMMV.