I've done a lot of philosophizing on the nature of units and there's a bit of an interesting wriggle there. Most people think "length" and "time" are different things, such that 1m + 1s = garbage. Mathy physics people* say "Aha! They're really the same thing, just set c (the speed of light) to 1!" This, then, raises an interesting question: is there anywhere you can't do this? In other words, is there some irreducible set of dimensions by which the universe operates? I tend to think no, since the units always divide out like this article says. But then, why are lengths what they are? Why did the universe settle on this scale? What even is length, and is "this scale" just an artifact of human perception somehow?

* The same mathy physics people also do fun things like define Gaussian units where charge is proportional to fractional powers of length and mass.