I would also hypothesize that they need less brain because they need far less sensory input from their skin and body because of their feathers. They can't feel

I would also hypothesize that they need less brain because they need far less sensory input from their skin and body because of their feathers. They can't feel their feathers directly and their feathers protect their skin from abrasion and cuts so their is no point to really good sensory input from most of their skin other than to differentiate feathers for grooming and tell if their feathers are being touched or not. A bird for example is not going to force its way into brambles or thorns that poke their skin or push through brush in search of food like a mammal, they either avoid the thorns completely or have enough feather protecting them to ignore certain types of thorns. If they get into a fight they are relying almost entirely on feathers to protect them and any cuts or abrasions are often fatal.