All of this points to using serial numeric IDs as both a unique key and the clustering key. UUIDs do nothing to help with any of those requirements, and generally hurt all of them. They do that because of certain characteristics they have that are specifically there in order to solve one of the few problems we didn't have to worry about.
Tangentially, in software systems design, I've long since realized that the word "always", when left to roam around freely, unchaperoned by any qualifiers to limit its universality, is an indicator of limited breath of experience. So, when you encounter it, it's useful to mentally insert "in my experience" as a stand-in qualifier. Having done so, the next conundrum is that "in my experience" advice is only actionable to the extent that you know what experience the advice giver has to draw on.
You are very wrong and wildly misunderstanding the problem that UUIDs solve
Yes, you should be sorting things by created_at. Having another index is not a bad thing.
> The weird id mixed up with index problem from the article is something which never happened to me ever in over 10 years of web development.
How do you know? It's a remarkably difficult bug to detect.