A lot more volatility, without a (or much smaller one) buffer most economic shocks would have a bigger impact on the economy.
Also there would still be a lot of inequality it would just be intra-generational.
Then again.. all the annuity money has have to go somewhere. So maybe the insurance companies would become the primary sources of investment capital (which wouldn't be great). A lot of uncertainty though i.e. buying a house if you have a family would become much riskier..