There's a bit of a straw man, in that argument.
He proves convincingly that not all life strives to have big brains. But he does not prove that big brain are not very desirable survival traits, nor that they are unlikely to develop where there is a functioning and evolving ecology.
Nobody expects that we will find planets where all life has big brains. Nobody expects that all planets with life will have any life with big brains.
There is even a term in the Drake equation to put a probability to this. You can discuss how large or small this term should be, but I never heard of anyone setting it to "1".