First, the goose that lays the golden eggs. I see the goose as the economy, rather than the working age population. The point is that redistribution may adversely affect incentives and thus reduce total product eg through effects of tax rates on investment location as well as work-leisure choices.
Second, how important is the demographic crunch? Its importance depends on how much birth rates have been declining – not so much in the US as Europe. It also depends on what else is happening in an economy. Its importance diminishes if productivity is rising rapidly, or if there is a terms of trade improvement (as in Australia in recent years), or if pension levels are relatively low etc.
You make a valid point about the relevance of the assumptions of public choice. Other factors are also relevant. When deciding what kind of public support to provide to the elderly poor I think voters would have some regard to the way alternative approaches might impact on their grandchildren if they were aware of the path dependency involved in universal PAYG systems. My point is somewhat Rawlsian – people don't really have much idea what position their grandchildren are likely to have on the income distribution.