I'm a lifelong imperial-ist but switched to metric after getting into woodworking. It was too tempting to do math in my head like "This piece is 13 & 3/8ths, I need to subtract 13/32nds and then find the midpoint of that..." and then screw it all up at some point.
Now it is just "This piece is 340mm, I need to subtract 9mm and find the midpoint: 116mm": relatively easy peasy.
That's not a problem with imperial (13+3/8 mm and 13/32 mm have the same problem); it's a problem with fractions (especially 'proper' fractions, which should never be used for anything ever, since they combine all the downsides of both decimals and rational numbers, with no benefit). Normalize everything to, say, 1/64 inch units and "This piece is 856/64in, I need to subtract 26/64in and then find the midpoint of that: (856-26)/2 = 415, so it's 415/64in." works fine.
If you "normalize everything" you get the metric system (up to a scaling factor): all distances are expressed in metres, all energies in Joules, all forces in Newtons, all pressures in Pascals, etc. Note that the latter are just naming conventions (for kgm^2/s^2, kgm/s^2 and kg/ms^2, respectively).
This can lead to some unwieldy numbers, e.g. "turn left after four million 1/64 inches", so naming conventions are often used, like "mega" for "million".
True, but 1/2^n fractions are highly encouraged only with imperial in my experience, and my problem comes in that my different measuring instruments give me different levels of precision, ranging from 1/8" if I'm using a big measuring stick, to 1/16" on my tape measure, to 1/32" on my embedded measure, to 1/128" on my calipers. And then there are times when you are given measurements in tenths of an inch which feels natural for most (13.2" long), and that gets ugly...
Probably if I was a better woodworker I would have a solution for this without switching to metric.
Er, yes, that was my point: the problem is with the fractions (and especially though not exclusively the 'proper' fractions), not with the choice of metric vs imperial for units.
Imperial explicitly endorses the use of all the weird fractions and measuring tenths of an inch with a measuring tape is simply not a thing that would ever happen in the US.
I hate converting between 3/8ths and 7/32nds all the time. It's such a stupid system, and I miss metric.
Now it is just "This piece is 340mm, I need to subtract 9mm and find the midpoint: 116mm": relatively easy peasy.