Gotta say, this just sucks. A world with the only free roaming mammals being humans and rodents, the rest gone or in a zoo.
I suspect the diminished insect populations would coincide with our own populations being reduced - I'm thinking of those predator/prey system graphs they use to introduce Differential Equations.
So a significant drop in our population may coincide with a rise in insect and other wildlife populations.
lol, im sorry, differential equations? Not saying you're wrong *shudders*, but you could have gone with 'food webs' which I suspect is something a lot more people are familiar with.
Related though, the best working example of how interconnected things are (as far as I'm aware) is Yellowstone and the re-introduction of wolves. Its an absolutely incredible success story, which saw yellowstone's ecosystem in crisis and verging on collapse being saved by adding back in the apex predator that we killed off. (Though the provided example of sea otters/urchins is a good one too)
To me, its the height of hubris to think we're ready for the effects of mass extinctions. Give it another couple hundred years and maybe we can turn the world into neat pastures. Kill off all the crap we don't need, make engineered analogies of "wildlife" that works the way we need it... But that is purposeful terraforming and biosphere engineering on a scale far beyond what we can do now.
Right now, we're just stomping around killing stuff in the way. Anthropocene is probably inevitable, but without intentional its just self-xenocide.