They argue that Peters' model produces extreme risk aversion in lotteries with (near) zero payoffs, and such risk aversion is not backed by empirical work or even by intuition.
"Would a person ever prefer a process [A] that, after three rounds, diminishes wealth from US$10,000 to 0.5 cents over one [B] that yields a 99.9% chance of US$10,000,000 and otherwise US$0? Ergodic theory predicts [A] [... but] [v]irtually everyone will prefer B"
That is, growth models don't behave well at or near zero.
Personally, I enjoyed reading Peters solution to the St. Petersburg paradox and how the ergodicity framework is applied to economics in such a concise and intuitive manner.
But I am reluctant to think that this ergodicity framework will completely remove the "psychological" aspects of economics. The utility of agents still needs to be accounted for. The ensembles that Peters describes are heterogeneous, and agents can derive different amounts of utility even if wealth or growth rates are equal. Think about insurance.