Unless something big changes, world population will start to fall in a few decades, after which it will most likely rise again due to insular fertile subcultures like the Amish. Falling population should then cause a more than proportionate fall in innovation rates, though that would reverse if we developed ems or human level AI. And that might fix most culture drift! Innovation rates likely fall before population does, due to aging and Africa being less innovative per person.
But even if population rises again, when will innovation rates rise again? Even if innovation activity stayed at the same levels of relative effort and effectiveness, its effect on the economy wouldn’t rise to its pre-population-peak level until the new economy rose to be substantially bigger than that level. But would innovation effort and effectiveness stay high?
Modern innovation rates are quite unusual historically. There were a few known ancient bursts of innovation, but they didn’t last long. Even in the last few centuries most innovation has come from a small fraction of the world, and in some of those places innovation rates seem to have greatly fallen from their peaks. All of which suggests that innovation-supporting cultures are fragile, not natural, and easily disrupted.
Innovation as a practice spread in the last few centuries because winning societies were especially innovative. This pushed losers to copy winning styles in many ways, plausibly causing the spread of innovation, liberality, and many other Western styles.
But after innovation rates greatly fall due to population fall, innovation will seem a less important social phenomenon, making less of a difference to who wins or loses. And then societies will less prioritize it, less sacrifice other opportunities for it, and less work to regain it when if randomly decays. Plausibly leading to widespread decline of cultural support for innovation. And also for liberality.
Then after several centuries of low cultural support for innovation, we might have a world population dominated by groups descended from current day Amish and Haredim. Then even when the population and economy again grow large enough to support current levels of innovation, given current levels of innovation effort and competence, that world might not actually have enough cultural support for innovation to induce such levels of effort and effectiveness. Having lost the taste and habit of innovation, the world might take a long time to revive it again, just as it took a long time for the ancient world to stumble into a way to create our current innovation levels.
That is, while the coming post-population-peak economy might retain many industrial techs, such as cars and electricity, it might lose the capacity to innovate such techs, and not rediscover that for many centuries, or maybe even longer. And a world with rising population and constant tech is much more likely to be a world of falling median income. So we may return to a world of poverty and low liberality, plausibly also with more war. A non-modern world, but with cars and electricity.
This is what is at stake, if we don’t find a way soon to either fix fertility fall, or develop ems or human level AI.
Note that some find hope in the fact that innovation supporting culture is rare and fragile. They say we might greatly increase innovation even as population falls if we could find ways to spread such cultures more around the world. But we have had many decades of local areas trying and failing to make themselves into the “next Silicon Valley of X”. Seems we just don’t know how to promote innovation cultures.
I don't think industrial society can exist without further innovation. Supplies chains are too complex, and things are always shifting, production without innovation is not possible. In order to keep our society going at even a reduced scale just requires too many engineers. If you have to train so many engineers you can't expect innovation not to happen. So I think society is more likely to colapse rapidly, or stay competent than to slowly decay or to hang on in a steady state.
I doubt current Amish culture would maintain a stigma on innovation for centuries. People will expand to fulfill niches. If only Amish are left, there'd be too much easy money in being the world's only big innovator, and people would inevitably defect from Amish culture to fill that niche.