VI would be IIIIII which is severely over-wide. The balance is really against VIII and XII, you don’t want one leg of that triangle to have a limp and IIII makes IV just a bid wider and chunkier to provide that balance. “Symmetry” was probably a poor choice of word this isn’t a mathematical thing but perceptual, those three points being equal visual weight evoke an equilateral triangle standing on its side which says “yep this won’t tip over, ever”, because, well, things shaped such don’t and the back of our head instinctively knows. Thus you get a sense of stability, and I guess this is a good example of why artists often sound like mystics or plain nuts (“this song tastes of strawberries”).

The IVPPITER explanation definitely also makes sense but it doesn’t explain why people continued to do it after standardisation on IV in arithmetic and the fall of Roman paganism.