It's true that (for example) a third of a metre isn't expressible accurately in decimetres, but you can always just say (continuing this specific example) "a third of a metre". Nobody will be confused about what you mean.
This is however perhaps a good argument in favour of non-decimal currency.
It doesn’t matter. Just write 333.333 mm and if you make it evident in your construction drawing that three of these third meter-things need to fit one meter somebody might even calculate the width of the blade into it.
Measurements are just a number and you will always have tolerances and chains of measurements to go with them to clarify what you expext as a end result.
Yes, good point - I was thinking about casual, everyday uses, but if you're going to be precise then the question of divisibility becames even less relevant. Just tack on as many decimal places as you need.
It's true that this applies just as much to non-metric units, of course! But then if divisibility isn't a big deal, this goes both ways - meaning that the disadvantages of the metric system's base 10 orientation may well be minor in practice, and not enough to outweigh the advantages.
(Actually though I think the metric system has you more cleanly covered for this sort of case, with its consistent set of prefixes for scaling up and down by 1,000. Non-metric units tend to be a random jumble of 8s, 12s, 16s, or worse.)
This is however perhaps a good argument in favour of non-decimal currency.