Medical professionals shouldn't carry guns. You're in the business of saving lives, not taking them.
in a perfect world where every scene was safe the yes that might be true, then again if the world were perfect there would be no need for ems or law enforcement for that matter. regardless, i think it's usually unwise to take an all or nothing approach to these kinds of things. there are a lot of places where it might really be smart to have ems carry guns.
9/10 times, pulling a gun on an already hostile person just makes them kill you quicker. If something looks dangerous, walk away and call for PD. If it is so sudden that you can't do that, chances are this is gonna be one of those 9.
ideally we would have police backup on every dangerous call. the reality is that police take a while to get there, and the places we respond to are dangerous. to say that you are always going to be able to just walk away and call PD is assuming a lot. despite the best made plans and care taken by yourself and your partner, the streets will be unpredictable... at least that's been my experience. just my two cents.