isn't it kind of moot? there are plenty of other rodents. They fill the gap left by rats. I'm not really sure eliminating all rodents would be a good idea for the ecosystem.

Rats are, to my knowledge, more destructive and spread more disease. Obviously eliminating all rodents would be disastrous for the ecosystem, but rats in particular are an invasive species in North America so eliminating them specifically doesn't seem like such a bad idea.