Metric and imperial don't change the way carpenters work because in the case you mentioned of a sub-mm dimension, that's in the 64th of an inch range. Carpenters don't ever measure to that precision because of the fluidity of the material. Craftsman will at that point just cut to fit.

My point with those hard numbers wasn't that metric would make those numbers easier, only that your examples were intrinsically favouring imperial measures. Maybe it's easier to say:

What's easier to figure out, 1/3 of 3cm or 1/3 of 1 93/512 inches? You can easily construct scenarios for a measure that are easy in one and obscene in the equivalent. It's less about the notation and more about the measure. If you assume all of the initial measures are round in imperial units, then the math will automatically be easier. If your designs were designed in metric, they'll be round to metric. If they're in imperial, they'll be round in imperial.

And when this degree of precision is actually important, imperial craftsmen (engineers, machinists) already use decimal. A "Mil" is a milli-inch.

Anyhow, again, I agree that for some very specific scenarios dealing with fractions is easier, especially when you're doing any base 2 operation.

I just think that you would be surprised how infrequently the issues you're imagining would actually manifest themselves, working with intrinsically metric designs, and that you're underestimating the number of scenarios where not dealing with fractions actually would make your life easier.