Talk politics.

It's not even really a case of assisted migration, of humans giving cats a hand in an expansion that was already underway. Cats weren't expanding, they got picked up and moved because they were useful to human agriculture.

It's also not a matter of difference in speed of expansion: cats aren't adapted to the jungles of SE Asia and Indonesia, which they'd have to cross to get to Australia, nor the bitter cold of Siberia, which they'd need to cross to get to the Americas. They would not have expanded at all without human intervention or having evolved so much that the colonizers would be a different species altogether.

Bad example: corn comes from the Americas, and it's actually a hybrid that can only survive and reproduce with human aid, i.e. it can't go feral (or whatever the term would be for plants).

Actually, it is a bad thing. The more diverse a biosphere, the more likely that there will be something with the qualities needed to survive any sudden changes in environment.

To give an example of the dangers of shallow gene pools, the Tasmanian Devil is on track to becoming extinct by 2035 because the combination of culling, introduction of foxes, and road-kill have reduced its genetic diversity to the point that it's one of only three species susceptible to a transmissible cancer (Devil Facial Tumor Disease). Regular virus and bacterial infections are similarly more likely to reach pandemic levels when a species lacks genetic diversity. Fungal infections wiped out the Gros Michel banana cultivar — at one time the major banana cultivar — and its replacement, the Cavendish, is in danger of becoming agriculturally non-viable in a decade or two because a strain of that same fungus that the Cavendish isn't resistant to has finally emerged.

All of the domestic species lack diversity, despite what one might think from the huge range of variation in dogs breeds. If you then turn around and replace other species with these low-diversity groups worldwide, you set yourself up for massive hardship when something pops up that can wipe out the very plants and animals we're dependent on for food and pest control. Preserving indigenous species and working to develop strategies to domesticate them to increase the variety of our own agricultural toolset is a far better strategy than simply replacing everything in the Americas, sub-Saharan Africa, and Oceania with Eurasian transplants that only have a few thousand years' worth of diversity accumulated.