Now, if i decided to give all of this to my hypothetical kids -right now-, potentially decades before I'm dead. They could grow up with it, invest it, make money, and be reasonably "rich" (not 1%, but better off than most) by the time they are in their 30s. And then they could give THAT right away to their kids, again, decades before they are dead.
Repeat the cycle. So my grand-grand-grand-etc childrens could be absurdly rich, technically thanks to me, but where do you draw the line between whats inheritance and what is not? I gave the money while I was alive (taxed and stuff, but still), they were the one who invested it and made that additional money through their own action (though it was super easy, it was still them clicking the buttons on their investment account's website, and according to taxes, they made it).
So how to you stop that from happening? I can't give money to my kids while I'm in my 30s?
Now ok, let say I can't give money. Instead I take my money and I spend it on private school, tutors, private college, etc. Even if living in a place where education is free, you can certainly have a lot of influence through money.
No matter how you spin it, somewhere down the road, this effect will compound. Starting from scratch in a videogame means you'll take longer to catch up than someone who's been playing the game for a while and twinked their subsequent characters. No way is it going to be different in a system as complicated as real life.
Actually, you don't need to draw the line. It's covered in the tax code. There's this thing called the "gift tax." People moan about the complexity of the tax code but a lot of it is there for a reason, so you can't just go AHA and pivot a little bit and subvert the entire intent.
If you give enormous wealth to another who is not a spouse or a charity, while alive, or while dead, then you (or your estate in place of your dead spouse) will, in fact, have to pay the taxes due.
The thing is the taxes are too low and the Republicans keep zeroing them out when they get in power.
There's pros and cons on the various ways they can happen, but it does not change the fact that the kid of several generations of successful/influencial/rich/whatever people will do better for themselves on average than someone fleeing a poor country who just came in this one.