Maybe it won’t then. Cities genuinely are an unusual habitat, and there are species that thrive there but not most natural environments. Dandelions for instance are a major invasive here, but when I get away from the short-cut lawns we provide, I rarely see them.
There are a few thousand other species of cockroaches than the German cockroach everyone thinks of first. Those probably outcompete it in the wild, and I’m sure they would manage as well or better without us.
I remember those from when I was a little girl, like early 70s. I really wanted us to have one, but mom said they were too expensive. Until the 80s we only had the big ones that Michigan Bell supplied for free.* Even after mom started buying cheapass phones in stores, we had dial ones long after places began requiring touch tone phones to access menus.