The big jump between units (mm and m) is really useful as even the most preoccupied of coworkers will notice if the scale is out by a thousand. If the units were closer -- say 10x -- then there would be more ordering errors. That explains the absence of centimetres (10mm) from construction sites even though centimetres is a popular household unit.
Millimetres dominates construction as being close to the width of a cut it is the perfect-size unit. It's simple to work with because you simply count: in imperial a tad more than 1⅜" is 1½"; in metric a tad more than 35 is 36.
Even though we retain the same size of timber as in the imperial past, those sizes are now expressed in metric -- common sizes are 90x35, 120x45. So you can measure up an old house for a repair and order in timber of the same size. There are not pre- and post-metric timbers.
For what it’s worth, 1/16” is also about a saw kerf. But in my experience, that doesn’t really matter because, as I was taught, you don’t take the line, but keep the blade completely on the waste side.
Like OP said, anyone in construction in Canada is using Imperial Measurements on the job site (even the guys from Europe). Just makes more sense somehow.
I grew up with both systems (Canada switched when I was a teenager) and to this day strangely still prefer Imperial for measurement, temperature, speed, and weight.