Earlier quoted context omitted.
No, it can't come from tax in general. The whole problem is a lack of productivity per capita. So any tax high enough to pay the shortfall will be oppressive. It's not a magic money machine that beats private investment earnings.
Your statement only makes sense if you assume growth. At steady state investments into e.g stocks and direct transfers is about the same thing. And ye, if the economy shrinks so will pensions. But that would be the case for stock investments too.
Re: Taxation, if you want to make up for the shortfall in people's pensions with an additional tax, you're assuming that someone else is making enough money to make up the difference. That is not the case. People can hardly fund their own pensions to the extent recommended, much less anybody else's. Most businesses are not profitable enough to fund extra pension contributions either, and imposing that cost will stifle them.