Cortex? OK - calling it that is a mammal thing.
Pallium? Lots of critters have one. What is a Pallium?
Note that the swellings of the neural tube into lobes has a bump that is called the telencephalon. That develops in different ways in different branches of the animal kingdom but birds definitely have one.
You may notice that the avian pallium has many of the same structures as the mamian counterpart. It is shaped and layered differently but I would not say that birds “don’t have a cortex” because we don’t call it that.
@gmirey may have some additional insight on this.
I would like to add that the efforts of the Numenta group has been a laser-like focus on the cortical column and it’s computation. What would be different if the group had started with the avian model? The two models are very different but achieve much the same high level functions.
This thread reinforces my assertion that the higher level functions arises from the connections of processing units and that the minor details of the local computation is not as important.
I see that the best way forward is to work back and forth between what computational functions that are provided by the low level structures and what high level functions emerge. Each line of research will inform the other on what is computational-level and what is implementation-level details. I see that focus on just one level will make it hard to work out the differences between these levels.