Libertarians, Republicans, and Rich People all seem to loathe the idea of the transfer payment. If they care about the elderly or others at all, they believe retirement should be funded by savings. This misses a very obvious point. However you structure your society, if the idle are to live, they must be supported by the labor of those who work. Savings or investment are just another means of transfer the product of one person's labor to another person.
The whole structure of human society is based on such transfers. That doesn't mean investment is a bad strategy for a society - it's actually essential for progress. I happen to favor incentives (or even compulsions) to save, but I don't think that's a way suitable as the sole funding for retirement. There are a few reasons for that, but one big one is the fact that it's highly pro-cyclical. In a recession, when more spending is needed, investment values tend to decline rapidly, leading to a contraction of spending and more recession. By contrast, government payments are at least cyclically neutral.
The really big transfer payments in our society, by the way, are to the rich and super rich, and they take the form of various exclusive licenses and rights to property that are defined, granted and protected by the government. Bill Gates is fabulously wealthy mainly because the US government gives him exclusive rights to certain intellectual property almost none of which he actually created.