One cannot claim that private retirement accounts are "the answer" because retirees will be able to draw on them for income (as this author describes), and then simultaneously claim that the amount of "drawing down" will be insignificant. That's trying to have it both ways.
The "drawing down" does not affect prices only so long as there are younger people coming along who are saving for their own retirements at about the same rate as the retired are selling. Then we have wealth being put on the shelf at roughly the same rate that wealth is coming off the shelf. So far as the economy is concerned, that's a wash.
The demographic problem we have is that for several years, more wealth will be coming off the shelf than going on. That is an increase in the supply of assets for sale, with no corresponding increase in the demand for retirement assets. That most certainly will affect prices. It will drive them down.
This issue is not about "money," or "funds," or any of that. It's about the human condition, and the fact that for almost all of history, the elderly were supported by a generation that was significantly larger than the generation turning old. "Zero population growth" means that doesn't happen anymore. There is nothing one can do with "money" or "assets" to fix that. Without significant growth from one generation to the next, working adults cannot produce enough actual stuff to meet the needs of both the young and the old. One or the other is going to suffer. I think it's clear what the correct moral choice is here. When my time comes, I will make it. I refuse to be part of a "conspiracy of the old" to beggar children. It's not my call, but I hope that the Lord sends the people who do that straight to Hell, when they do finally die.
I've read the opposite.. With projected longer life spans, seniors won't be able to stay out of the job market or the stock market unless they manage to hit critical mass.