While it would definitely and drastically increase the viability of Earth to eliminate mankind, it's an invalid statement to make and assumes mankind is not of the animal kingdom.
Human karma is to burn carbon for power and change ocean salinity. 85% of the species alive in 1900 are now dead. We are technically in an extinction event. And as soon as other animals evolve to invent hydroponic grow systems they'll be just fine. Humans will live in bubbles on Mars before they die off, and at that point might the earth would be decimated.
Peace?
There is a definitive trajectory of intelligence and how that relates to existance. The tipping point seems to be be both complex language and tool making coexisting. The rest can be done through observation. Humans have a defined role.
800,000 - 30,000 BCE - Migration, Interbreeding, and eradication of competition.
30,000 - 10,000 BCE - The final glacial procession of the ice sheet forces humans into areas closer to the equator.
Around this time the wobble of the Earth's procession dried up the Sahara and much of today's desert belt forcing people to condense by water.
5,000 BCE - 1900 CE - The growing pains of advancement. Trying various ideologies and forms of control to run a more perfect society.
1900 - Future - Refining in reference to the Kardeshev scale. There are levels of progression with the scale shifted.
Type 00 - Using the immediate resources. Thinking locally. Laws impact confined areas.
Type 0 - Using a much larger area requiring peaceful exchange of goods and currency. Thinking in relation to trade benefit. Still segmented. *You are here *
Type 1 - Using the resources of the world requiring an even more widespread peaceful relation. Thinking whats best for the planet. One world government required.
Type 2 - Using the resources of the universe. Requiring an almost godlike consideration for place therein. Thinking whats best for life itself.
There needs to be something to push humans into a type 1 society. Something so ingrained it requires genetic recoding to change. No amount of forced ideology will ever bring peace.
And now I have spent far too long on this answer, and goddamnit you banned him already