He isn’t personally wealthy. The Bin Ladin family is. If he was a loyal family member, he would never want for anything. By flipping the finger to dad, he lost that access.
And again. He never did anything wrong. His only obligation is to live his own decent life.
You don’t run around correcting all your fathers mistakes... do you?
If my father were a slave owner or a Nazi, I’d feel some obligation to make amends, to the extent that I’m able. It looks like Omar is doing that at least symbolically by traveling to Israel. But “running around” is a bad choice of words, and so is the word “mistakes”. Eichman and bin Laden didn’t just make “mistakes”. They deliberately set out to kill as many people as possible. One should be conscience of one’s heritage. Just like a father can leave you a fortune in property, he can leave you to deal with a vast legacy of iniquity that you can and should deal with.
Going back to the scriptoral quotes, the Talmud teaches that G-d does not punish children for the sins of the father, so long as they do not take up their fathers’ misdeeds. Eichmann’s oldest sons carried on their father’s tradition, and remained avowed Nazis. The youngest was, I think, an engineer and publicly renounced his father. He did not take up his father’s misdeeds, and even rejected them. But the deeds remain. The dead are still dead, their stolen gold teeth still smelted into gold bars. That’s a whole lot of bad karma, and some sort of effort ought to be made to counterbalance it.
I’d distinguish that semi-obligation on direct descendants of evildoers from the idiocy of CRT, that holds all white people responsible for slavery and Jim Crow and condemns them irreversibly, and all the evil that flows from it. Basically, it’s Nazism with a different master race, looking to inflict fresh crimes on humanity. But some sort of balancing of the books ought to be at least attempted by the direct descendants of mass murderers. Not because anyone’s forcing it or demanding it, but because that’s the right thing to do. Karma and all that.