It was a variant of i that made its way into codices in the Middle Ages to make the "i" clearer and more distinct. The fact that it is pronounced in so many different ways shows that it wasn't created to represent a particular sound, ja?
Feels we are talking past each other. Literally this is what happened.
Introducing systems of recording ideas is a completely different and far more organic process than attempting to artificially dump a new character into an existing system that doesn't need it. I can't think of a single instance where the latter has succeeded.
The J sound is not new, but the J letter is what only 500 years old?
You are correct it started as a variant I symbol, but it became a popular enough symbol that we started using the J letter for multiple sounds that existed prior and were used to be done in different ways, we all swapped to this new way. This does not happen often but this does happen.
And while it happens in languages (rarely), it also happens in other systems as well where we use symbols to communicate ideas. For example mathematical notation, scientific notation, computer programming has their rules of syntax of both words and sentences change quite frequently. So while in writting / language the notation rarely changes, it happens far more often in other ways ways to use symbols to communicate ideas. For example the standard way to do algebra equations X+Y+Z=A+B+C and while there were predecessors it was Rene Descartes who popularized this notation with algebra / math in the last 370 years or so.
For the other sciences the "syntax" changes are even more recent and they are ever changing, for example with modern programming languages the syntax rules are such that you may "evolve" a language or create a new language altogether.