Because that is what happened before collective pensions. When people talked of "the poor" until the 70's, they talked about older people.

Then you need to first prove that it was the fact that the pensions were collective that fixed this issue, and you then have to prove that it will revert if they get uncollectivized.

Because most workers have little enough disposable income that they can't save a lot of money.

Well, evidently they can, since they pay for the collective pensions. That money doesn't dissappear just because the pensions aren't run by the state.

Because it is hard to know how long you'll live as a retired person

And this becomes easy if your pensions are collectivized?

and individual insurance contracts are much more expensive than collective ones

That's not true. When Sweden got a pension system in the 50s, people who were self-employed could elect to not pay to the collective pension system, but instead pay to private pensions. These people have gotten much higher returns that the state pensions. So in fact, it's probably the other way around, as it usually is.

insurance companies have to forecast a winning on each contract.

So? Despite the fact that private companies always have to go with a profit, private companies also always provide the same service cheaper than when the state does it. That there has to be a profit does not make it more expensive, it's a red herring. What makes something expensive is lack of competition.

Because having to put your earnings into equities, as is needed for individual pension plans, puts you at the risk of market crashes.

Which is easily controllable by gradually moving over the savings to safe investments with low returns the closer you get to retirement age. Hence not a problem.

Because unions and the state are democratic institutions, unlike the market.

You are using the word "democratic" as in "majority rule". It is true that they are democratic in that sense. That means that with unions and the state, the majority decides over your life. I don't see how that automatically means that old peopl become poor, but you are welcome to explain.