This paper starts by assuming that the different neuron density of birds vs non-avian reptiles is due to birds being endothermic. That's... quite an assumption

This paper starts by assuming that the different neuron density of birds vs non-avian reptiles is due to birds being endothermic. That's... quite an assumption. EVERYTHING about the evolution of birds is about flight. Specifically, it's about keeping weight down. Loss of teeth, for example, is a tradeoff where birds have worse digestion in exchange for losing the weight cost of teeth. Birds frequently get leg injuries because of how small their legs are: again a tradeoff between durability vs weight. Seems to me the first burden of proof for this theory is to show that birds have wildly more compact neurons due to endothermy rather than the usual weight issue. Their own data is not helpful to their point as it shows differences between bird clades suggesting significant evolution on this point since the initial evolution of birds.