Only three species of animals on Earth make tools: elephants, chimpanzees (as Jared Diamond would say, humans are the Third Chimpanzee), and New Caledonian crows. Meta-tool use is considered crucial in the evolution of humans. And, yes. New Caledonian crows are there. The crow’s brain size as compared to their body size is comparable to many primates. As such it is appropriate to think of them as feathered apes. And, then there is their social structure, which is more like human social structure than that of any other primate – enabling a leap forward in evolutionary cognitive development.
You have to watch this: A Murder of Crows, NOVA (sorry, this is just a preview).
It won’t just be cockroaches left after humanity self-immolates. I would bet crows will survive. And, give it several million more years of evolution, and the crows will fill our niche.