If we killed all the bad people, like the violent thugs and whatnot, would the world really become a better place?

Probably woulnt work
But lets start in the morning anyway;)

No one would be here.

We all sin. Only God is good.

We are given free will. Satan still roams the earth.

No. People always find ways to cause conflict...people always disagree.

When you say "if WE killed", Who is "we"? Who would do all this killing? And what makes you think you'd be in the group doing the killing, rather than the group getting killed?
If 50% of the human race killed the other 50%, then everyone left alive would be a murderer.
Would that be a better world?
An eye for an eye leaves the whole world blind.
Violence is not a solution to violence.

Not until you address the conditions of life that make people become like that in the first place. It's not some genetic thing that you can wipe out by killing everyone with certain personality traits. People are shaped by their environments. If you kill everybody that's been shaped by an unjust world but leave the injustice that made them that way in place, all you've done is make yourself into a mass murderer, for nothing. So long as poverty, exploitation, oppression, bigotry, war, and so on exist, then people will continue to be shaped by those circumstances.

There's also the fact that one person's perception of a "violent thug" or other form of "bad person" is almost always shaped by his/her own experience and prejudices and may differ drastically from other people's perception of the same. Nobody thinks of themselves as "the bad guy", but for all you know, you just may be the one, killing people you judge to be bad based on your own personal prejudices while leaving a blind spot for others that you don't see that way (perhaps including yourself) but whom others may see that way and for good reason.

To illustrate my point, take for example this comment you made:

"By we I mean, well, the police, maybe us the civilized people, the victims of those horrible acts that wronged them etc?"

Who are "the civilized people"? Throughout history it's often been those who regard themselves as "civilized" and others as "uncivilized" who commit the most savage acts of all, convinced of their own righteousness. The British Empire, the Nazis, the Romans, the United States, the Japanese Empire, the Spanish and Portuguese colonialists, and so on. What makes you "civilized" and others not? This is what I mean. Frankly it could very well be the inverse.

As for the police, there are reasons why some people (primarily middle-class white people) identify the police as the "good guys" but others may not see them the same way. For example, take the fact that a black man is murdered by a cop every 28 hours on average in the United States, the vast majority unarmed and defenseless, shot in the street for some arbitrary reason. Police are people like anyone else, shaped by their environments, and their role in enforcing a power structure over other people makes them the agents of that power structure's prejudices and injustices. Cops are often corrupt, brutal, racist, historically have often been a prime base of support for fascism and apartheid in various countries (and of course then serve as the enforcers of such), and so on. So, you can't just say "the police" are "the good guys" who are going to help wipe out "the bad guys". To many, the police are the most violent of the "violent thugs" you speak of. Police reflect a ruling social system, which may often be unjust, and they will then reflect that injustice.

"The good guy" to one person may well be "the bad guy" to someone else who has a different experience with the same person, due to a different position on the social ladder.

Isn't that what Antifa is trying to do?

I will get bored for sure...nothing else to do...