Since we can map $\mathbb{R}$ to $\mathbb{R}^4$ and back, is the 4D spacetime merely a simplification tool or a fundamental aspect of the universe?

Since there exists a bijection from $\mathbb{R}$ to $\mathbb{R}^4$ , it is trivial to see that the entirety of physics can be rewritten unidimensionally. You can say that the coordinates of any point are actually just a single value on $\mathbb{R}$ , apply your physical laws on the values as mapped to $\mathbb{R}^4$ , then invert the mapping to get your answers expressed entirely in $\mathbb{R}$ again. I don't think the fact that the bijection is not homeomorphic matters here. Now obviously, this is convoluted. But is there any fundamental reason why it can be said to be an erroneous view as opposed to a merely more convoluted view? In other words, is there something more fundamental to the 4 dimensions of spacetime that I'm missing here, or does it only boil down to "you can easily express the universe in a single dimensional way, it just adds pointless extra steps to your math"?