I started https://wordsandbuttons.online as an experiment in zero-dependencies architecture. No third-party, no self-reference. Every page is completely independent. I was told, that as it grew, it would inevitably become impossible to maintain.
Five years passed, including a two-year pause for writing a book. I did more than half a hundred interactive tutorials and quizzes, and continue to add them when I have time. The thing simply refuses to go "too complex to maintain". All the maintenance problems I ever faced with this design were handled within minutes. If there is too much typing, I write a Python script. If not, I do the change manually, replicate it in a few pages, and go on.
As a free bonus, since all my pages are essentially hand-written, no dependencies = no uncontrolled growth, they are all fewer than 64 KB each. Ultra-fast to load, and I never get a "Reddit effect" since even 1000 requests a second is only 64 MB of data. It's green then tea too. I usually have a few hundred thousand visitors a year, and they barely consume enough electricity to boil a kettle of water.
I think this rule of three, like many others is just an attempt to escape well-known complexity issues by putting them under a carpet of less known complexity issues. I'm very happy to have ignored it when considering design for my site.