These failures of the system also mean that the poliece cannot be trusted as your only source of protection and sometimes you need to take things into your own hands.
Great. And then what'll happen to you? Doesn't matter if the system's a mess, if it refuses to let anyone who goes beyond it unpunished.
Beyond that, outside of superhero media, vigilantism is not going to work. Clearly it's something people can abuse: and if you can't trust the system to reliably differentiate between a justified and unjustified case, how exactly do you expect that to end?
As for the racism thing, that's just a distraction from the real issues. There are stories about white cops killing black people but those stories would have never been in the news if it was a black person killing a white person, a black person killing a black person, or a white person killing a white person. Killing happens, and just because it sometimes by chance is a white person killing a black person doesn't mean anything. Here in the U.S. you get funny looks by mentioning that someone is black, the only racism here that's a probelem here is caused by people taking non-racism too far to the point where they discriminate against the inherently racist white people, but even that is very rare.
Intra-race murders tend to occur because of geographical closeness/accessibility, there's nothing particularly stand out there. Certainly, some people may be oversensitive: consider that's because
there is something there to be sensitive about. You get funny looks mentioning race in the US because you've convinced yourselves you live in a post-racial society, that there's no need to acknowledge race because everyone's treated equally... It's a way of neglecting responsibility.
I honestly don't have the time to go in depth into race relations in America, accept it or don't, the fact remains some people are demonized, some people are not, whether or not you believe some of it is race based. With an unbalanced court system, there is no way for guns to work in practise, even if they worked in theory.