Basically every other species reproduces only because we allow them to and it benefits us. If we were ever existentially threatened by a competitor, we would eradicate it from existence before it even became a legitimate threat. Single-cell organisms and viruses are the only things we struggle with totally eliminating for our benefit, but we're working on it.

Trying to eradicate would change the environment and conditions and would favour species that are resistant to our eradication attempts.

I agree that there's no plan or roadmap, so maybe I was not clear in my wording. What I mean is that given infinite time, a smart species will tend to emerge, and when it does, it will be the most successful one. So evolution (by random chance) converges to higher intelligence.