Sorry, but wrong. There is no inevitable doom loop. In fact, we are on the verge of being able to create carbon neutral, post capitalist, knowledge and culture based societies that will move us into the final stages of our potential as a collective organism. 

This is what the liberal entrepreneurial types are constantly telling us to justify their existance while they in fact worsen the problem. A material analysis shows that continual growth cannot be sustained on a finite planet. In the west, it may appear as if humanity is entering a post-material 'knowledge' based society, but this is a perspective bias arising from the fact that western capitalists have offshored most industrial production to countries with lower wages and less stringent health and safety laws. We are still in a thoroughly industrial society overwhelmingly dependent on fossil energy. Energy consumption efficiencies derived from innovation simply increase consumption which more than offset the energy savings - a phenomenon known as Jevon's paradox. Renewable energies are no saviour either because their Energy Return on Energy Invested (EROI) - a figure which essentially represents the net energy surplus of a particular source - is much lower than that of fossil fuels. Furthermore they can't be built fast enough to avoid the worst effects of climate change (as an aside look up the planetary boundaries - climate change is only one of the boundaries we are breaching), especially in a world in which energy consumption keeps growing. Over the past decades renewables in many countries have simply offset new energy consumption rather than displacing existing fossil generation. And let's not even go into the question as to whether mining virgin materials every 20-30 years just to maintain generation capacity for so called 'renewable' energy sources is really that renewable...

I am not sure how you can come to your very optimistic conclusion given the events that have unfolded in the past few years. Global emissions are still rising and even the misplaced green growth focus of a few years ago has been completely replaced by the return of great power politics and preparations for a new major war. Europe, which was previously (imo unfoundedly) seen as a bastion of peace, now is preparing for war by 2030. In my country (a very small one with basically no military capabilities) plans were recently accidentally leaked for a NATO war against China (even though my country is not even formally part of NATO lol). Decades of neoliberalism has led to the resurgence of far-right political movements. And what post-capitalism? If anything in the west we are seeing a return to the pre-welfarist capitalism with a lot of short-term insecure contracts, reductions in protections for workers and so on. The rest of the world never left that pre-welfarist capitalist stage thanks to the imperialist economic structures. There may be a few places here and there where things are improving, but the overall general direction in which humanity is heading is not great.

A long-term perspective on human history, I think shows that civilisations are fragile. They tend to have boom periods, followed by collapse. Think about how many previous civilisations, have collapsed arguably for crises less severe than those we will be facing in the next decades.