This assertion makes no sense. Debian Stable has always the paragon of stability to the point that it's actually criticised for it. The Debian Testing release is even famous for being more solid than other distro's stable releases.
Breaking changes in Debian are practically only remotely possible in Debian Unstable or if you purposely install packages from backports or PPA repositories that have no assurance of stability or even maintenance.
Maybe you meant debconf? When I was a DD it was an RC bug if your package used debconf to do "magic", i.e. using it as a registry for an application, or not properly re-seeding answers from the configuration and assuming the debconf db was the source of truth.
That's a fist-full of caveats. Arch is willing to upgrade the kernel, maybe you should include a dist-upgrade in the comparison.
I can plan for it? You can see if you're upgrading your kernel. Nothing breaks if you decide not to run an upgrade.
This nonsense is why stable and LTS releases were introduced in the first place.
If I'm faced with a major upgrade of an LTS system, I usually choose to reinstall from scratch, shedding packages I haven't needed for a long time with it. But that happens every couple years or so.
If you're okay with hitting the forums now and then to find out why your desktop has been behaving oddly the last two weeks, rolling is your thing. You won't have to break in your new dist-upgraded or freshly installed system for like two weeks.
If you don't want to play lottery every time you hit enter for that update or if you're a business where you can't afford possibly breaking all your laptops for some security update, stable is your only option.
It's "choose the best tool for the job" I guess.
This goes back to my original point, which we've drifted a little from.
Ubuntu has more unexpected behaving when upgrading than Debian.
A working dist-upgrade should not be something that your OS struggles to provide. Asking people to reinstall their OS isn't an acceptable answer.
Upgrading should not be a lottery.
This argument that you MUST dist-upgrade as soon as the next version is available, and completely ignore the entire idea around LTS, is silly.
This idea that you never want to upgrade from one LTS to the next is equally ridiculous. Upgrading the operating system is part of the package manager's job.
I like Linux, I don't dislike dealing with the OS. But I want to deal with it on my time. Expecting to get work done and then realizing something is broken and being forced to deal with it is a completely different proposition from picking out a weekend to reinstall your work PC with the newest LTS version.
For a long time before using arch I thought too that rolling release might be more unstable, but I have come to the conclusion that quite the opposite might be true.