In general when people worry about inequality, except the most radical commentators, they worry about a trend, not about differences in net worth.
Maybe unconsciously, PG try to sell the idea that this a binary thing, you have 0 inequality or you should leave the market do its thing. This is not true. There is a balance and we have a lot examples that show that.
The pie thing don't pass the smell test, neither.
Is PG denying that the pie is now bigger than in the 70? I don't think he does, actually he is arguing the opposite.
Then why low and medium income people is increasingly in debt and have to worry if tomorrow will have enough money to pay the rent?
When you have a bigger pie, and inequality is the same, you get the rich more rich and the poor more rich. This is hardly what we observe even if we know that the pie is bigger.
So, the pie is bigger but people should to work more hours and should retire latter, and, of course, we can't afford healthcare for everybody.
He says "let's attack poverty, and if necessary damage wealth in the process."
I totally agree there, good luck with that.
Piketty shows (with data, by the way) that, below a percentage of economic grow, capital returns are bigger than labour returns.
The conclusion is that there is a trend (very important, it is a trend) to bigger inequality inherent to the system.
What do he propose? A communist revolution? The abolition of inequality by the proletariat?
No, just tax capital so we can redistribute it to all the society.
Of course, if you are a billionaire (except maybe Warren Buffet), you are always to be in favour of "laissez faire", that is, in favour of not changing anything. We are just right now like we should be. Everything is perfect, we don't want to kill innovation.
Of course, a bit trickier if you don't have capital, but rather have plenty of tangible goods. In which case, they'd probably ask you to submit your "profit and losses" for every year, keep track of how much you made in each year, and start taxing you based on anything that means your running total goes above the magical threshold.
Any who, the point is. They will find a way that they will claim is "fair" and consistent but probably has loop holes, and figure out a way to tax capital.