Writing the above comment got me thinking about agents having different discount rates for different sorts of goods. Could the appearance of hyperbolic discounting come from a mixture of different rates of exponential discounting?

I remembered that the same sort of question comes up in the study of radioisotope decay. A quick google search turned up this blog, which says that if you assume a maximum-entropy mixture of decay rates (constrained by a particular mean energy), you get hyperbolic decay of the mixture. This is exactly the answer I was looking for.