Ok.
If you know that a marginal hour of labor will produce benefit that can be put in a private account that is for yours to keep, then people will work longer.
Why would they work longer? I don't see anything in your reasoning to support this hypothetical syllogism. I mean, your conclusion does not follow from the premise. Some people might well prefer to go fishing. It only takes one to spoil the argument.
As I said, it will bring about people chaning their labor input and also will make people more risk-averse and people will engage in risky activities less and less.
Again, this requires quite a leap. Will a twenty-two year old high school graduate be more or less likely to be a risk taker than a forty-five year old high school graduate?
This seems to assume a level of rationality I simply do not believe we commonly share.
It doesn't matter what individuals may do, it is what people do in aggregate that matters. In the aggregate people have to behave rationally, otherwise we will notice massive dis-equilibrium in the economy, which we don't. In fact, a lot of honest behavioral economists will admit that in the aggregate people are a lot more rational than we think they are.
I will tell you why people will work longer. Keeping wages constant, if the marginal output of labor increased your marginal wages/wealth you will increase the output of labor. In countries with high taxes, people also work less. People work a lot longer in countries with low taxes. If your marginal labor will be taxed at a higher amount, you will consider all your other elasticities before you commit to the extra hour of working. Maybe you would rather go fishing than have govt take 60% of what you would make if you worked that extra hour.
Social security represents such a tax. Govt borrows at a real rate of .86%. So, when you work an extra hour you know that 12.4% of your earnings will give you .86% on average. If you knew that it will get a higher return, then it represents a tax-cut. People will allocate labor more efficiently.