Problem-causing fits usually starts from extreme values of \tilde{y}. The following plot from this issue shows sometimes simulated datasets (green, y_sim#7 and orange, y_sim#20) are at least a hundred times bigger than the real-world dataset (red).
Rejecting them is computationally beneficial as I observed those extreme fits (y_sim#7 for instance) could take 100 times longer, but I think we should keep in mind this additional action hurts the theoretical support from the SBC uniformity proof.
