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.
My whole point was that the "cockroaches will take over the world" thing is built on two points. The nuclear survival one, but also the ubiquity of cockroaches around human habitation. The entire world population of wild cockroaches which aren't dependent on humans is a very small proportion of the total number of roaches.
The vast majority of cockroaches by numbers are entirely dependent on human civilization (probably something like 9999/10000 of all roaches). Sure, some cockroaches will be left if we die off, but a tiny fraction of the current population numbers, and almost none of those will be the species we normally interact with.
You're just being pedantic and ignoring what I actually meant. For example when people say e.g. "all the cats will die out" they almost certainly mean the domestic housecat species, even though technically, a lot of other things are cats, too. By your argument, everyone would also need to qualify any statement about cats since they could mean pumas or caracals or something, which are types of cats. Similarly, when I said cockroaches will die out once humans die out since they're associated with our urban ecosystems, naturally, I was talking about the common species of cockroaches that are assocated with humans, and as I pointed out, these are the ones people are talking about when they discuss cockroaches, not hypothetically Andean Tree Roaches or some such.
Actually as far as I can tell it is built on an apochryphal report that was adopted by the anti-nuclear movement and made into the meme it is today. See, for example:
https://slate.com/news-and-politics/2008/07/will-cockroaches-really-be-the-last-survivors-on-earth.html. Although the original sighting (if there was such and it is not just an 'urban legend') was likely to be from a pest species of cockroach there is no guarantee it wasn't an early recolonisation from a non-urban species.
Thing is that even the pest species of cockroach are far from dependent on human civilization, yes they profit from it in terms of population density but they are more than capable of surviving without it. Looking to Wikipedia for three of the four common pest species (the fourth is lacking relevant information there) it is noted that their diets are:
"German cockroaches are omnivorous scavengers. They are attracted particularly to meats, starches, sugars, and fatty foods. Where a shortage of foodstuff exists, they may eat household items such as soap, glue, and toothpaste. In famine conditions, they turn cannibalistic, chewing at each other's wings and legs."
https://en.wikipedia.org/wiki/German_cockroach"American cockroaches are omnivorous and opportunistic feeders that eat materials such as cheese, beer, tea, leather, bakery products, starch in book bindings, manuscripts, glue, hair, flakes of dried skin, dead animals, plant materials, soiled clothing, and glossy paper with starch sizing. They are particularly fond of fermenting foods. They have also been observed to feed upon dead or wounded cockroaches of their own or other species."
https://en.wikipedia.org/wiki/American_cockroach"[The Australian cockroach] appears to prefer eating plants more than its relatives do, but can feed on a wide array of organic (including decaying) matter. Like most cockroaches, it is a scavenger."
https://en.wikipedia.org/wiki/Australian_cockroachI don't think any of these species will have difficulty surviving without human civilisation. In fact although their numbers would almost certainly decline longer-term in a post-nuclear scenario in the short term they are likely to explode in numbers due to the abundance of rotting human flesh as a ready food supply.