Well here's an article to deflate a lot of balloons! I liked your version, which sounds just as silly as the official version.

The history of the Holy Trinity goes back the Council of Nicea in 325 AD. While Christianity had spread throughout the declining Roman Empire, the movement was beginning to splinter. The powers-that-be---both secular and nonsecular---thought it best that only one version of Christianity would be better.

So the Council deemed a certain version was to be front and center. This version latched on the Trinity, based on some rather specious interpretations of the various Christian documents of that time---and here we are today. Most of the offshoots of the Nicean church cannot shuck aside this theology.