So the state should seize mom and pop shops when mom and pop dies? Then what? Try to sell it? Have it as state run enterprises? Now every generation must completely pull themselves up from zero, and the state seizing all value every time someone dies? Parents die accidentally - too bad for kids, the state seized all value and sent the kids into some state system.

Countries that seize this much property don’t do too well economically.

When the owners of a husband and wife shop die, with no inheritors, then what?

If the children of the mom and pop shop die, and the children are preschool aged, with no other inheritors or people designated to handle the estate, then what?

Effectively no one says that "every generation must completely pull themselves up from zero".

Do you seriously think the children of working/labor class families, living in rental housing, and with no capital, completely pull themselves up from zero?

Since they don't, neither do the children you hypothesis. So what's the point of your argument other than to tug at our heartstrings about those orphans?

Oh, and if the mom and pop shop is bankrupt, or has little capital, and there isn't family or close friends able and willing to take care of the kids, then who will?

Oh, right, "some state system." So if you are so concerned about these children, perhaps we need better orphanages and better support for the foster system.

Now, how do we fund those improvements?