If getting a million dollars wouldn't affect how much money you can leave your kids, you already have generational wealth.
Well said.
Where I live, one million dollars would allow me to pay off my house, open healthily sized investment accounts for my kids, pad my investment account, setup a trust and, overall, set my family up for a comfortable life in the future. I don't see how that isn't generational wealth.
Basically the bar is higher than "something you can pass down". It is enough that the next generation does not need to worry about making money either.
We can debate “live comfortably” if you want, but no 4.5 people are doing that from the investment proceeds of 1m.
What you are describing is kind of more like social mobility.
Generational wealth is definitely not "affect[ing] how much money you can leave your kids." That's an equivocation - if you're leaving your kids a dollar, another dollar will "affect how much money you can leave your kids."
edit: you need a million dollars to securely retire at all, and that's if your parents, kids, or you don't get sick. If they do, a million is not only not "generational wealth" but it may not even last you three years.