It is important to note that the unfairness you describe doesn't affect the positive (non-normative) observations of bias-preservation that the blind hiring approach persists.
Now, pivoting to moral claims along the lines of your comment:
Discrimination has a long history, of which slavery, carting to reservations, redlining,and so forth favored certain groups consistently above others, in the past and in the present. In my view, repairing at least the present entrenched bias by any name is in order, the question is to what level. Autarky is a feasible outcome, if desired, which is to do nothing. The diffusion of favored and privileged status will always feel like discrimination to the group that had favored status. There is still a moral imperative to at least correct current entrenched bias, which in the US can show up in incarceration rates, ability to invest, etc.etc.
Unless you feel these groups that are historically and currently biased against are somehow responsible for their own situations? If that is the case, autarky or favoring your personal situation has a basis to build on. However, I fail to see how various denigrated groups through time brought their current biased outcomes. You've been shown evidence by other commentators that in the US blacks receive longer sentences than whites. Is that just how it is, or do we have as a society a moral imperative to fix at least the current system, let alone offer historical reparations?
Anyways, you didn't answer why people must be considered as groups instead of individuals? That seems to be the only lens you consider people, while also only choosing the group identity of the most perceived victimhood over an arbitrary time frame. And again, if you want to say that someone takes on the wrongs experienced by a group, then they must also take responsibility for the wrongs committed by the group. So in your example about US blacks, that group also commits the majority of crimes so they must acknowledge and resolve that too. Are you prepared to say that?
You're changing the argument into something about morality but the reality is that there is no cosmic justice. You can be born with missing limbs, or to a destitute family, or inside North Korea. The best we can do is make sure that if you work hard (and yes, harder than others who might be born to a billionaire US family) that you get the same exact chance to gain a position because you are actually competent and qualified for it, and what you look like and what some group in the past has done has absolutely nothing to do with that.
Perhaps what's most insidious about ascribing group victimhood is that you must also accept the converse, which is group responsibility. Are you suddenly going to be held responsible for any wrongs that your group has ever committed? Are you truly certain that's what you want?
You are ignoring that life is not fair, and never will be. We cannot control the bodies and circumstances we are born into. But every individual has the ability to make the most of their opportunity and achieve their goals, and quite a few in history have proven that they are able to accomplish far more by effort and will than any natural advantage otherwise. That is the best we can do, and unless you create some matrix world where we are all exactly equivalent clones of the same capacity, that is all that is possible.