Dynasties only work if every generation buys in to continuing it. Ideally, by adding more to the family balance sheet than they take out. All it takes is one generation to completely ruin the ladder.
There's the saying, "Rags to riches to rags in three generations," and I think there's a lot too it. How we can avoid this unfortunate pattern is another matter, but it all has to do with living within your own means and earning what you spend, instead of standing on the shoulders of a parent or grandparent.
As far as me goes, I fully intend to be FI and reasonably wealthy long before anything happens to my parents. My grandfather is still alive and in reasonable health, and every so often I get papers indicated that I hold shares in various mutual funds here and there. I'm grateful for them, but they don't change any of my financial planning. I want to earn my FI on my own without any unfair advantages.
When my parents do pass, I should be in my fifties or so, and they should have quite a lot of money. I suppose I'll donate a lot of it to various charities and scientific research. As for the rest, I am not sure. In fact, having a lot of money scares me a little bit, because I know just how quickly one can take such wealth for granted, and start to get hobbies in yachts, gambling, and other things.
I think a good rule of thumb is to only hand money down to members of the next generation if they prove themselves responsible and stable, and they're middle aged. I can agree with helping younger people with schooling and perhaps the first home buy, but to build self-esteem, self-confidence, self-reliance, and the sort of ethos that builds and preserves wealth, I just don't think it's a good idea to keep giving and giving and giving and giving.
EDIT: I'd like to elaborate on the fear I have of extreme wealth. It scares me a bit that right now I could go out and buy a car in cash, or that my parents could buy two or three more houses and keep them empty, et cetera. I guess the way I mitigate it now is by not thinking about it very much, or by looking at those numbers in the bank account as purely numbers, rather than indicators of what luxuries I should or shouldn't indulge in.