Native cockroaches are nothing like the invasive urban ones. The ones people mean when they say cockroaches will survive a nuclear blast aren't "bush" roaches as we called them in country Australia, they're the 1-2 species of worldwide urban ones. The German Cockroach and other big city ones will nearly completely die out once humans are gone.
EDIT
https://en.wikipedia.org/wiki/Cockroach
There are 4600 cockroach species, but only 30 are found around human habitation, and only 4 of them are notable as being pest species, all of which are introduced species. Those species will all mostly die out when humans are gone, they are dependent on our ecosystem.
So cockroaches aren't cockroaches? I'm not buying. Bush roaches are cockroaches too!
The quotidian reason for thinking that cockroaches will take over the earth in the case of a catastrophic nuculear incident is their purported immunity to radioactivity, and although that contains a large degree of falsehood (as the wikipedia article you quote evidences) that was not the basis of your argument, which was expressly about their dependency on human urban ecosystems which is patently false.
(Even in the case of urban cockroaches I suspect that they are not 'dependent' on the urban environment but merely thrive under those conditions, hence the 'mostly' in your quoted statement - but this is beside the point...)
Making the argument that cockroaches aren't cockroaches is just hilarious.
--------------------------
Separately a study currently in the news demonstrates some worrying information. Microscopic plastic fibers (and shards and balls) have been repeatedly found in rainfall. Including in about half of the samples taken from a remote mountainous site.
The implications of the pervasiveness of the dispersal of plastic in the contemporary ecosystem are disturbing.
'It is raining plastic'
https://pubs.er.usgs.gov/publication/ofr20191048