World population growth is going down, and is currently nearly static in high and middle income countries (it would actually be negative without immigration, looking at birth rates; nearly the entire first and second world are below replacement fertility rates).
Sure, growth is slowing down, but it's still growing. I've heard that we're due to level off at 11 billion. My point is we're overextended RIGHT NOW. We're having increased global deforestation, half of all wildlife has been eradicated since the 70s, ocean health is getting worse and we're STILL GROWING. Here are some sources on the ecosystem being diminished:
As for the socialism v. capitalism thing, I'm not saying either would preserve the environment. My point is I think the very core of capitalism makes it impossible. The purpose of capitalism is to maximize profit for those with capital, correct? That means exploiting any and all resources. Taking a more reserved or long term sustainable approach means you fall behind and can lose competitively to those who are more aggressive and can capitalize in the shorter to medium term. This means an almost maximum use of resources. Socialism doesn't necessarily mean that. It CAN mean that, like you mentioned, with fulfilling quotas, and collectively agreeing to come to a similar outcome.
My point was neither one obviously solves the problem, though capitalism appears to accelerate the problem as much as possible.
Going back to the deserted island scenario. Say we realize that if we overfish we won't have enough food for the year, here are some ways of handling it:
Ideal socialist approach: Everyone votes and collectively agrees to impose limits on how much we will fish, so we can continue eating all year.
Likely socialist approach: Everyone votes that they don't want to reduce how much fish they eat, because they like fish, so they will continue overfishing until there aren't enough left, people starve.
Capitalist approach: Steve fishes as much as possible right now so there will be more for him, but Jim and Charles also do the same so that Steve doesn't get all the fish. The fish are depleted rapidly, people starve.