The current 'old' also inherited a built environment and a great deal of basic research, and if you project back far enough (not far!) they barely paid anything for it either. Those working in the 40s and early 50s paid almost nothing (in terms of having to pay taxes for other people's benefits) for the infrastructure that they inherited.

It also somehow suggests that the bulk of historical economic activity was the development of long-lasting capital works that outlived the users, which is odd.

I think we already have enough spurious arguments for feather-bedding relatively well-off old people without inventing weird new ones. The monumental voting power of the old has ensured that they collectively do pretty well for themselves; astoundingly well, say, compared to children living in poverty.