The fact that you subdivide investment and consumption into a variety of categories doesn't change the fact that you still need to tax one or the other.

Piketty's argument is that allowing wealth to concentrate in the hands of a few is the biggest threat to the stability of modern economic systems because it ultimately means that less money is available to everyone else, which restricts growth.

This is incorrect. Piketty doesn't make any claims at all about less money (or less wealth) being available to anyone. He claims merely that the ratio of worker income to capital stock will be lower than it otherwise might be. Please, go read even just the introduction to the book.

Further, he hints that that the richest people will have the highest rates of growth of their investments (the book is pretty weak on justifying this, again, academic papers might be better). That means the best way to actually create wealth is to put money into their hands. Note that if the richest people do not have the highest rates of return, then there is no reason to expect wealth concentration. See my blog post which works out the math on this in detail.

Note that I'm actually citing the math in Piketty's book, not his mood affiliation.