I feel like the other answers are missing some very grave points: We are not just reliant on the planet, infrastructure, technology, etc, it also relies on us. It relies on us too because of how we have shaped the world today. How long could a nuclear reactor run for before something very bad happens if you take away humans?
When losing humans, you will also lose the capability to manage some absolutely vital processes that are currently going on in our ecosystems. A nuclear meltdown may not affect the entire planet, but all nuclear reactors, dams, etc. will destroy the current state of the...