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.
At a more sane expected return of 5% annually, you get $50k a year to live off of to just keep what you have (or rather, watch it slowly erode in value due to inflation).
That is basically a one person income, maybe two adults if you pinch pennies and live in a crappy apartment or a low-end house in a midwestern suburb.
You can get a lot more lucky with a million bucks than you can with 10k if you gamble, but there are no guarantees. Risk tolerance is the most impactful variable. For those in the low risk tolerance group, I think you'd need at least 2 mil these days. And that's with being frugal, as well as probably not having much left over for kids.