"Just fine" is an interesting word for a post apocalyptic world.
What about all the nuclear reactors that we let melt down?
When a society collapses, no one will be there to shut them down.
It's possible that abrupt chaos occurs and shit hits the fan in the manner you're thinking. Coronal mass ejections / EMPs that destroy the electric grid of regions/countries/the world, nuclear blasts, pneumonic plague-like disease, etc. Mass chaos/die offs where we don't have the "right" people to shut off reactors/handle waste, etc.
I think that catabolic collapse is far more likely. Societies will stop funding advanced "1st world" types of things, in order to keep basic systems running. As societies start catabolizing themselves, don't expect functional democracy, expect dictatorships and foreign wars over resources. This leads to less resources for things like new school buildings and new school books, research and development, etc. It leads to further crumbling infrastructure that doesn't suit the needs of maintaining basic systems like water, food/transport, electric. It's all a positive feedback system, so the more you catabolize now, the less you have later to catabolize. I imagine that nuclear reactors will get switched off and waste disposed of as we switch back to coal or oil and even wood power, until the electric grid itself becomes too much to support due to limited resources and skilled manpower.
So, "just fine" is relative. They'll be much better off than the poor huddled masses when you can no longer get fruits, vegetables and meats just by driving a few miles to a store, as they'll have stocks of foods and the manpower to create and run little bunkers for themselves. They'll have electric generators and inverters, gasoline, diesel, propane stores, and of course armed security to protect all of the land they gobbled up with their hoarded wealth. And I'm sure they'll offer the starving peasants the job of farming the land they own for a small cut of the yield.
As the
feudal lords ultra wealthy land owners consolidate their property through alliances and marriages, their
feudal estates property holdings will grow, with the
serfs poor non-landholders working the land for benefit of the landowner, and their own subsistence. The
knights armed security forces will get more privileges awarded to them by the ultra wealthy land owners (gotta keep the guys with the guns happy), with highly-favored armed security personnel getting small plots of land for their own as payment for their loyalty. Other armed security personnel will know that with their loyalty and good luck, they too can one day be a feudal lord...oh shit, did I say that last part out loud? I meant to say they too can one day be a wealthy land owner.
I mean, we've seen this story before, and if you look around without being blinded by all the flashing lights and crushed candies, you can see where we're heading.
You and I might not live long enough to see it, but there are people alive today who are going to get to experience it. Sure, we could mitigate by managing our remaining resources intelligently so collapse is much slower and perhaps some miracle like Cold Fusion comes along to save us from ourselves...but counting on it is not a very smart move. Expect more "we're going to start to make small changes here and there that won't affect the rate at which we're burning down the planet...in 5-10 years". Expect more, "well, we're already at X.X degrees warming now, but to really prevent the apocalypse we just have to not get to Y.Y degrees warming, so let's keep turning oil into water bottles and fluorescent taco holders".
Or, I'm just paranoid, and Elon Musk, his SpaceTesla™, and wind turbines built into solar panels attached to wind turbines are going to save us from a planet we are literally setting on fire for short-term quarterly profit reports and amazing shareholder returns. I'm sure there are some people who can argue that smart contracts ran on Ethereum 2.0 will also help prevent climate change, ocean acidification, and top soil depletion, but I digress.
This cartoon shows it concisely, in my opinion.