Kickers do kickoffs, extra points, and field goals. Besides that they're not on the field. The only time hitting a kicker is allowed is if it's some sort of fake play where the kicker ends up running with the ball. Even then, there tends to be a gentleman's agreement where teams won't rough up the opposing kicker, as doing so means their own kicker is fair game.
I knew one guy who was a kicker for a PAC-12 team (back when it was the PAC-10). He said he was hit only once in 4 years. Earlier in the game he'd insulted someone on the other team, and the next time they were both on the field, the guy hit him from behind long after the whistle blew. That's not really a football injury as much as it's a violent crime.
As far as I'm aware, no kicker has ever been found to have CTE (though the sample size for them is very small), and their concussion rates are much lower than average. I think the studies on kicker concussion rates overestimate how often they sustain head injuries, as they likely incorporate data from less competitive colleges and high schools where kickers also play other positions.