There's a couple of different reasons conservative comedy doesn't work, although that is part of it. It's made worse by the fact that so many conservatives are more anti-Other than they are pro-humor. A lot of them have the mistaken impression that the quality of a joke is measured by the number of people it offends, which is not so much comedy as a coping mechanism for being an asshole.
Compounding this is the fact that the modern Republican party and by extension many of its voters have no real ethical framework outside of, "win no matter the cost." And related to that is the plague of disinformation that forms the life's blood of conservative media outlets like Fox, OANN, Newsmax and The Daily Caller. What you end up with is an audience who sees comedy as another front in the culture war that they have to win. And as you yourself pointed out, violence is the rhetoric of choice for people with more anger than wit.
As defenders of the status quo, conservatives are particularly resistant to change and while they identify a few societal problems correctly, for the most part they just make up fantasies about how persecuted they are by time moving on without them. Other people's problems can be boiled down to cliched answers like, "personal responsibility," and, "tradition." Which makes any kind of humorous sociopolitical commentary borderline impossible.
Perhaps the biggest problem of all is that modern conservatives live in such a bubble that they can no longer even agree with everyone else on what is real. To write good comedy, you need to be able to see the absurdities in reality and how they interact with the mundane and that which we typically take for granted. You need to be able to process complicated ideas like irony, without which sarcasm is just saying things in an off-putting way. Without a solid foundation of agreement on reality, communication with the audience becomes impossible unless they are approaching the material from the same angle as you are. The people who go to see conservative comedians aren't looking to laugh about the absurd. They're looking for someone to tell them they're right and everyone else is the problem.
And I guarantee that at least one conservative will reply to this post in a manner that will prove at least one of these points.