I used to think that too, but the problem with gun ownership in the US tends to be more about gun culture than ownership. Other countries with high gun ownership rates don't have nearly the same problems, especially when it comes to accidental shootings.

The problem of law enforcement killing people also has little to do with gun ownership. The frequent (or at least frequent enough to be concerning) shootings of unarmed black men for example are generally excused with police officers saying they were "afraid for their lives". This can only either be explained with terrible training or plain old racism (i.e. black men seem more threatening by default to the extent that an unarmed black man is considered more threatening than an armed white man), or most likely a mixture of both.

There's a lot wrong with how police in the US is trained and held accountable. Gun ownership is the smallest contributor to that problem.