Strange that they need water to reproduce, yet are found in deserts lol. I believe you though. I'm familiar with florida living and there are roaches everywhere, rich or poor.
I think that's why they need water to breed.
They are smart, they won't lay eggs if there is not water nearby, as having babies during the dry season would stretch limited water rations that are already low, to abysmal.
Its their way of determining season most likely. As desert climates, or at least Pheonix pretty much has Dry and Wet season like Madagascar. Monsoons flood the desert, but the rest of the year its so dry your spit dries before you get it to the ground lol.
It actually makes perfect since they require water to breed, if you think about it like that.

. Other than the desert Belt in the US they are native to Iraq, Iran, Arabia, etc. They are only native and wild in desert climates. Despite people thinking they will infest in Florida, but they don't and are not wild there. They may jnfest your Florida home, but thwy are not invasive in florida, but are badly in pheonix.
We can see that via their EOL page.
All Cali, AZ and Texas, mostly AZ.
Inat shows some in other areas of the US, but still drier areas and not 1 roach sighting in Florida, despite what the common thoughts are on roach forums.