A most likely bad solution to "Old Money"

We all see spoiled little children running around, doing whatever they want. And we all see spoiled young adults running around doing whatever they want.
A conversation about class inequality during my visit to UNL got me thinking. Most people believe, along with the statistics, that its much more difficult than capitalism's founders planned it to change classes. If you are born in the lower middle class, you are most likely going to die in the lower middle class. If you are born in the upper class, you are most likely going to die in the upper class. Sorry idealistic republicans, but it just didn't turn out the way Adam Smith planned it.
Our races and genders determine to a certain extent (hopefully a decreasing extent) how easy we are going to have it in life. Unfortunately, this is a very tough thing to change. We can't feasibly erase certain fundamental physical characteristics, and I don't even think we would want to.
However, the class we are born into has arguably as much if not a larger effect on how easy we are going to have it in life as well. But this, like race and gender, does not seem to be quite as tough of a problem to solve.
Capitalism is founded on the idea that those who work harder get richer. And society attempts to make this more so the case by offering education funding to lower classes and minorities. We want everyone to have an equal shot, because that is what capitalism is supposed to be founded upon.
So why do we allow for disgustingly gigantic inheritances? I put forward the radical proposition that upon a person's death their money goes to the government. Repeal the death tax? No. Make it 100%. This could allow us to lower other taxes--a pro-capitalism move. It would make every adult (sure there would still be spoiled children) have to work for their own money--another pro-capitalism move.
Why not do it?
Objection 1: The whole reason a lot of these people want to get rich is to ensure their children have a good shot at having it made, not having to work as hard as they did, etc.
Response: Well, then this has the added bonus of stopping the drive of so many people to get ridiculously rich (which, logic dictates, causes others to get poorer), thus shrinking the rich to poor gap that has been growing for a couple hundred years.
Objection 2: Parents will just give large monetary sums to their children before they die, which will not stop the problem.
Response 2: Yeah, that is an issue, but I'm sure there could be certain restrictions that would ease this kind of issue.

Alright, I haven't thought about this through completely, but it did cross my mind and I see no immediate HUGE problems. But, maybe I am missing something.