Because of the bumpy history of innovation in the past, Robin predicts a bumpy future - with a coming transition to an era in which the GDP-doubling time may be roughly two weeks.
I think another model is both more obvious, while still being consistent with the data:
Simple innovations are found first, with more complex and difficult innovations following. Early innovations can have a large impact, while later ones are more likely to be small, incremental changes. In a connected world, big and important discoveries can only be made once - and then they are forever off the table. We've already had the invention of sex, the invention of culture and the invention of engineering. Nature's inventiveness can't continue with ground-breaking discoveries forever. Later discoveries could in principle still have relatively large impacts - but after a while, this becomes less likely.
This model is similar to what we see when looking at the progress of data compression over time.
This "low hanging fruit" model of innovation predicts a bumpy start, followed by more gradual and incremental progress. This is not to say that there won't be any spurts of innovation in the future - but they are likely to be milder ones.
Obviously, this doesn't make for such a dramatic story as the one Robin Hanson tells - but I think it is one that is much more likely to be right.