I don't see why it isn't fair to people keep the wealth they create and just divide up the wealth created by the planet equally.
Now say I have fifteen children, and you have one. In the next reallocation, do we really divide out the land such that my family ends up with fifteen times the land your family has? Think about the incentives that kind of scheme creates.
Furthermore, there's a tragedy of the commons problem. If we all own the land, or it gets re-divided every generation, I have no reason to improve it. I'll get rich turning my land into a toxic wasted dump, because I don't have any interest in maintaining its value.
In the end, that's why we have property ownership. People don't take care of things they don't own.
You can let everybody rent their land, according to its value from the state and distribute the income equally. That way the land will be used efficiently.
The incentives that creates are better than the incentives we have right now. Either you pay eye watering rents to the state to live in a house on the immensely valuable land of downtown San Francisco or you yield the land to a property developer who will build high rises that will match the massive demand there is for people to live there.
There are more (and better) solutions to the tragedy of the commons than just privatizing everything and, as we can see, people don't necessarily take care of the things they do own. Anti-dumping laws exist for a reason.
Where people manage to enable themselves and their offspring to grow their wealth geometrically at the expense of everybody else they always do so by using (legal) means of siphoning off both natural wealth and wealth created by others.
If you inherited a chunk of stock which your parents bought which grew in value and paid out dividends since they died, for instance, that increase in value is real but it wasn't created by them or by you. Who did create that wealth is context dependent (most of the time it's going to be employees working for the corporation), but the fact remains that it wasn't you or your parents.
The same applies if you inherit a bond portfolio (the wealth is created by the people paying you interest) or land titles (in, e.g. a large city, that wealth is created by the people who live and work surrounding that land).
That's largely what is driving the inequality Piketty is measuring. 90% of the 0.1% siphoned all their wealth from others (e.g. alice walton types) and created none themselves and, IMHO, all of them siphoned most of the wealth they hold - even the ones that are dubiously considered 'self made'.
I think by aiming to create a system where the people get to keep the wealth they create and share the wealth nobody created (and the wealth created that isn't so easy to attribute), inequality will naturally decrease to a more sustainable level that people will consider fair.
In practical terms this means legislators should be encouraged to raise taxes on the very wealthy who very obviously siphoned wealth money first (e.g. the Duke of Westminster) before going after the wealthy where it isn't clear how much they created and how much was siphoned (e.g. the estate of Steve Jobs) and developing better ways of separating 'created' from 'siphoned' so that they can be treated differently.
Why, do you not think that's fair?