Probably a significant quantity of decomposing matter not being cleaned away and becoming more and more noticeable.
Also they convert that to nitrogen so our soil could be less fertile if they weren’t around.
There are many species of cockroaches, most of which aren’t pests to humanity. Just living their little bug lives out in the wilderness munching stuff. And getting eaten by insectivores in large quantities.
Humans wouldn’t notice much at first, but things would seem off and get worse over time. Disappearing animals - birds, reptiles, fish. Angry frog owners pacing back and forth. Orkin men begging in the streets.
Nothing bad
think of all the jobs that would be eliminated (exterminated?) if there was no need for cockroach traps/spray!
Lots of unemployed exterminators.
My pet tarantula would probably be a bit sad.