How can you suggest that we should "Forget whether they come from deprived backgrounds or are criminals". You seem to be suggesting that we should selectively focus on one element of the situation, which is that they are black, and forget everything else that is relevant? You can't be serious.
If more blacks in the USA commit crime, then it is hardly surprising more are involved in such incidents. The more serious point is why do the statistics show more blacks committing crime. Socio-economic circumstances, educational attainment, welfare dependency, being born to unmarried couples or to a single parent, urban-gangsta culture and such like would seem to form part of the explanation.
Except that often, and this is the key thing, the people getting killed have committed no more crime than something like a broken tail light, or playing with a toy sold in the store where the shooting took place (there has been at least one example of a youth/kid getting shot because he was carrying and playing with a toy the store he was inside stocked).
If it's so dangerous that the first response during a routine traffic stop is to shoot the driver multiple times because the he is moving his hands after you've asked for their papers (unless they're Jean Grey or Charles Xavier they're going to move their hands when asked to produce something), then either they need to get rid of the officers that are so worried they shoot just because someone is doing as requested, or make sure that officers don't go around on their own so they won't be as nervous about stopping a guy who is in a car with his wife and kid.
It is not a good thing when you're in a situation where a large part of the population actively fear the police and even more distrust them.
And unfortunately that is the situation that seems to be the case in the US, in part due to massive legalised (and then largely ignored) racism within living memory, and a system that means if you're anything other than white you're far more likely to end up in jail for minor offences.
IIRC for the same crime by the time people have been arrested, charged and appeared before a judge a black suspect is at least twice as likely to end up in jail - not for major crimes like murder, or rape, but things like possession of small amounts of narcotics (I think several studies have shown that for the same crime, with the same previous record you were at least twice as likely to end up in jail if you were black).
It's also not helped by the lack of any form of real comprehensive complaints procedure that has to be followed regardless of where you are, so in many areas if you make a complaint you can't do so anonymously or to a third party, but it's to the same officers who work with the person the complaint is about and may have no training in how to deal with them. Which means that because it isn't unknown (especially in some areas) for officers to not just get away with abusing their powers but to harass those that made complaints in the past you don't get complaints made for fear of things getting worse.
For all it's faults the IPCC, PACE etc have made policing in the UK much more accountable, and meant that it's far harder for a bad officer to remain in the job regardless of if he's in the MET or a local beat officer in rural Devon.
The US police in some regards seem to be stuck back around the point we were in the 70's with regards to accountability for their actions.