The whole "centralized, trusted repository that has all your apps" system is wrong at a fundamental level.
The way shared libraries are used in Linux is built upon the assumption that package managers and centralized repositories are the right way to do things.
I've done it both ways. Centralized works a LOT better. It's not even close.
You get a more stable system, and you get security bugs fixed faster, and more reliably.
What you lose is access to the "latest and greatest", because it takes time for the new stuff to filter in. And that's OK.
Depends on the distro. Archlinux is pretty fast to update packages.
The thing is, the distro maintainers need to decide whether they want a fast moving "latest and greatest" approach, which might break stuff by accident, or go a "slow but always dependable" route, which you can depend on as company, with painful losses if things go south (in which case there should be an express lane for important security fixes).
In my opinion, the reason why Archlinux can be so dependable is that packaging is based on really simple ideas, like not starting or stopping services on installation like Ubuntu would, and that most if not all system files belong to a package. The package manager can do a whole OS installation just by installing the basic packages on a directory different from /. The package format is also really simple. Getting into the guts of Archlinux packaging is really approachable and that makes me feel at ease for whatever trouble I may find myself in.
I've had my drive fail, but that was the drive's fault, and even in that case I also didn't need to reinstall everything. I just copied the good files and reinstalled only the packages whose files got corrupted.
If I sit down in front of my PC and can't do work, it's broken. That I can spend an hour or two fixing it rather than reinstalling is irrelevant.
Certainly, Arch is definitely not a "it just works" OS. It's a tinkerer's OS. Different distros favor different types of users. By what you said, probably something like Ubuntu or Mint is better, something that "just works" with minimal learning curve for someone not familiar with Linux in general and that does not wish to invest the time in learning it. (Not saying that you're not at least familiar with it, but that's what these distros optimize for, I believe.)
Personally I didn't experience all that much breakage, but eventually got frustrated by kernel updates breaking hotplug kernel module loading until reboot because Arch removes kernel modules for the running kernel. This breaks random things like plugging in a USB drive unless you happened to load the module previously, so you're essentially forced to reboot every time you upgrade the kernel or take care to manually exclude it.
I'm grateful for Arch because their wiki is beyond excellent, but I wouldn't recommend it to anyone unless they just want to tinker.
Is your supposition that a "misconfiguration" just "happened" randomly over night?
No, it's a rolling release distribution, software on it will break randomly on updates. You need to read their FAQ, even their official document will tell you this happens and it's not their responsibility due to the rolling release nature of the distribution.
If that's not it, then I've no clue anymore about what you mean as broken.
The work done in Nix and Guix is interesting in this regard.
Traditional package manager conflate having something with composing something (everything is ambiantly available and interacting). Nix separates those, so you can have every version of everything, and only try to compose things that fit.
I don't want a middleman, I want to get my programs from the developer, and store them using the tools I know (regular files on a filesystem).
Are package managers easy to use (most of the time)? Yes.
Are package managers (as they exist today) a universal, well designed way to distribute software? No, because they impose a middleman.
Also, for the most part, the "Arch is unstable" thing hasn't been true for a long time. I find that it's far more stable than Debian or Ubuntu LTS on my machine because of newer kernels containing newer hardware drivers.
As a Debian user, I appreciate that the stuff I install had at least gone through some minimal vetting first. And if I have to add a third party repository or download something myself to run, I'm much more likely to view that as the possibly-dangerous action that it is, and try to actively assess the reputation and trustworthiness of what I'm installing.
That's certainly not an average, noon-technical user thing, though. Vetted app stores are there to help average users avoid malware, assuming they're doing their job properly.
Things like the app store, in for profit scenarios, seem like ways to slip in monopoly control. Brew is an attempt to circumvent it.
I don't want to come across as suggesting they're a bad idea or don't have advantages, just that on balance I've always had a sense there had to be a better way.
Package managers are an easy way to do things, most of the time. That's why brew exists.
They are not a universally good way to distribute and install software. It twists the relationship between the software developer and the user.