[hortense]

> A perpetually inverted pyramid would require that fertility rate shrink even further, until it approaches 0

That is incorrect.

[otagekki]

A sub-replacement fertility rate will worsen an inverted pyramid situation, until the population eventually reaches 0

[slothtrop]

Given a constant fertility rate over time any inverted pyramid would eventually straighten out.

[hortense]

If you take a constant fertility rate of 1, you'll always have an inverted pyramid, until there's no more pyramid.

(I'm assuming that the life expectancy does not change significantly)