I have a feeling it won't happen due to the way the assets are. A lot of this money is unrealized, and can't be realized in practical terms. What we end up with are massively wealthy individuals holding companies (fiat assets) rather than real assets like land. Part of what drives inflation is the demand. If most people have relatively low incomes because most of the money creation goes to a few, then there won't be increased competition for the masses. Basically the wealthy people are in a different market in many cases and the inflation of securities wouldn't be accounted for in the CPI.

These are just my own thoughts.