That is somewhat idealistic view on SI, and even more so of the metric system. While SI is nominally coherent, it is in practice accomplished by having very awkward values for defining constants, and that factor is excluded from the coherence consideration. E.g. to convert from seconds to meters you need to use conversion factor c, which is very much not 1.

I would also be very careful and not conflate metric and SI systems. There are all sorts whacky metric systems (although most of them historical) that are not nearly as clean as SI. And even SI historically has been messier than its today.