Here is another way of looking at things:

1. From the inside it looks like automating the process of automation could lead to explosive growth.
2. Many simple endogenous growth models, if taken seriously, tend to predict explosive growth at finite time. (Including the simplest ones.)
3. A straightforward extrapolation of historical growth suggests explosive growth in the 21st century (depending on whether you read the great stagnation as a permanent change or a temporary fluctuation).

You might object to any one of those lines of arguments on their own, but taken together the story seems compelling to me (at least if one wants to argue "We should take seriously the possibility of explosive growth.")