You generally get wealthy by providing goods and services to others. The more you satisfy people's wants and needs, the wealthier you get. The wealth means that these people now owe you.
If you accumulate wealth instead of consuming it, you never take them up on it. You are basically acting altruistically - instead you use their IOUs to provide even more goods and services for others (not yourself) by managing your wealth instead of consuming!
I think it is actually an amazing feature of our civilisation. Wealthy people generally don't use their wealth to build massive monuments to themselves - they tend to invest it into economically productive enterprises that make society wealthier overall.
People only value the capacity to transfer wealth inter-generationally to such a degree so long as its required to guarantee your children don't live a life of endless toil for meager subsistence wages.
2. I suspect that no one in this discussion (even those whose words suggest otherwise) want it to be so that you literally can't leave anything to your children. So there's some point in accumulating whatever amount you can leave to them.
3. By and large, I think people accumulate wealth mostly in order to have it. I'd rather have $3M in the bank and know that barring really major upheavals I never have to worry about being poor, than have $0 in the bank and live precariously from one payday to the next. This would be true even if I had no children and no prospect of ever having any. It would be true even with a decent "safety net" ensuring that even if I completely ran out of my own money I'd never be, e.g., at risk of starvation or homelessness.
[EDITED to add:] Wait, there's more.
4. You might accumulate wealth in order to use it for some expensive enterprise. Consider e.g. Elon Musk, who (at least the way he tells it) got rich in order to save the environment and give us the ability to escape to Mars if we need to. I don't know what Warren Buffett's original motivation for getting rich was, but his present alleged intention is to give away almost everything he has for charitable purposes, and he explicitly says he doesn't want to give his children too much. (Though it may well be that "too much" in his sense is much more than 99% of parents could possibly give their children.) The advantage of this sort of use of wealth is that it doesn't suffer from diminishing returns as much as spending the money on yourself does. There's not much I could do with $2B that I couldn't do with $1B, but $2B will save approximately twice the number of lives that $1B will.
5. You might want to turn your wealth into power. Lots of lobbying. Carefully targetted political donations. Make yourself a household name and run for president of the US. Give funds to academics and other potential public intellectuals who happen to have views you want to be more widely heard. With a couple of billion used carefully you can have a big impact on your country, or even on the world as a whole.
[1] Or, of course, it might not; it could be, for instance, that the smooth running of a modern economy depends on a level of acquisitiveness that could never exist if people were getting money only for their own use and not their children's. (As it happens, I think that's unlikely.)
I had all this, thankfully, even without my parents being rich. They grew up in a time and area where they could still buy a decently sized house and have children on a single income. They struggled, but they made it.
Thanks to living in a (more) socialist country, taxpayer money paid for my education, allowing me higher social mobility than my parents. Ten or so years into my career, I've paid what was invested in me by the other tax payers a few times over already.
