That logic isn't sound.
It's actually incredibly sound. Things police have that make their day-to-day safer than it is for the average person:
The uniform signals their social status, which will scare most people from acting up in their presence.
They're allowed to open carry which will inflict more fear to prevent most people from acting up around them.
If they feel the need to, they're allowed to discharge their weapon on someone who they feel is acting up, and as we see, usually with little to no consequence, so they have less fear of pulling the trigger or inflicting any sort of physical injury on someone else in a situation that they deem requires "self-defense" than a civilian would have (a civilian executing honest self-defense would have next to noone to back him up and would have to explain himself in very hard
They also tend to travel in pairs, at the very least. If they're alone they're able to get in touch with their buddies pretty easily to get armed backup - how many careers let you do this?
When there's a violent situation, say a school shooting, the police don't charge in lone ranger - they wait until they have all the cavalry in place and feel like the situation inside is calming down and that they now have as close to 100% control of the situation as possible before entering, so when they do enter, chance of any of them getting injured or becoming a casualty are slim to none. Meanwhile, everyone inside has no means of protecting themselves, and are waiting for the police to save them... risking life and limb while doing so.
Being a police officer really isn't that unsafe. There's a reason a lot of them can get out of shape, have terrible aim, be horribly uneducated, and still be considered successful officers - it isn't so much what each individual officer is capable of that matters, it's the technology they have, the fact that they're empowered to use force and often protected from the consequence of that so they don't have to second-guess before using the force they're been authorized to carry out, that makes them good at what they do, and that they act as a large group. The main reason they have so much power is because how much they've taken away from the people. If more people were free to say, open carry, and fire on an officer who was carrying out a crime without fear of getting raped by the justice system (which I think might've happened with the Eric Garner situation if people weren't terrified of doing more than filming), more individual police would actually have to be good at their jobs in order to earn their status, and then yes, since people had more power to fight back against corrupt police, then policing would actually be a dangerous job.
At least, as dangerous as it is to be a civilian amidst police these days.
In reality, being a minimum-wage laborer is a far more dangerous job. You're going to be told to do things that are completely unsafe (get on a roof without a harness, work on that roof by yourself which means if you fall noone's there to call it in, etc.), and aren't allowed to say "No, I won't do that" because then you'll get replaced by someone else who is desperate for work and you won't get paid.