I am pretty dead set against what I know of CRT so far. I think Python and Scoolbubba have both made some good, long, posts highlighting the concerns that I have with it.
That being said, I don't think it is as simple as "What you do defines you". I think that it is a somewhat true statement. But it is incomplete and not nuanced enough. I think we have to realize that the deck really is stacked against a lot of people in this country. Many of them are black. Some of them are white too. I think we have to acknowledge though that skin color has played a role in the history of this country in perpetuating the cycles you mention in your post, and that by some measure it was intentional.
As someone who was raised upper middle class, had college provided for, two parents that looked out for me etc, I absolutely know that I had huge advantages in life that others did not have. Some might call that privilege, but my parents had to work hard to do that, and I have had to hold up my end of the deal and work hard to provide for my own family now.
Conversely, I've worked in settings in which I saw the polar opposite and how the cycle of poverty truly traps people. Do I think I should have to apologize for what I received and they didn't? Not really. It is the way it is to a certain extent. Are there ways we can try to improve these problems in society? Absolutely. Is there a simple broad strokes answer like CRT? Heck no.
The problem with CRT as it is currently being advertised is that it puts all people on trial: it presumes irredeemable guilt on the part of white people, and presumes innocence on the part of minorities. If anything I think it will fan the flame of racial tensions more than help. But I think it is also helpful to consider that CRT is a reaction to historical injustices that still perpetuate themselves in some cases today.