It does matter, because all the saving and dissaving of the saving-based scheme distorts financial markets and sometimes doesn't work anyway. For example, imagine a system where everyone buys an extra house, then sells it when they retire. Now there are twice as many houses as there need to be. And therefore everyone has to commute 1.41 times farther on average; twice as much lumber is used up; twice as many builders are needed. Now imagine the next generation invests in something other than houses because houses are too expensive because of all this extra demand. Let's say tulips. So the first generation goes to sell their houses to retire and... wait, nobody wants one? They already have one and they don't want to buy a second one for their own retirement savings? Well, then the housing market crashes and all those people lost money on their retirement. (And the third generation will buy up all these cheap houses and say screw the second generation's tulips, we don't want tulips...)
I naively assume that if you buy an extra house as investment, you rent it out. So the house is actually being used, no need build extra houses or have a longer commute.
Blindly investing and then assuming that it still has value when you retire has a lot of risks. This sometimes happens with owners of small shops who hope to retire with money they get from selling the shop.
