I know this is besides the point, but I've always been so happy that there are no cockroaches where I live... In fact so happy that I write comments like this, just so people know.
Cockroaches are not a welcome addition into your house's ecosystem, but they are still very useful in the global ecosystem, same as mosquitoes, etc. There are waste products that only cockroaches digest, there are plants that only mosquitoes pollinate, etc.