Aren't imperial units considerably easier to calculate on the fly in construction and when squaring? They seem to come more natural for me.
Depends. they are designed so the whole units are easy for the common things you do with that size. this is a common case for things will still do today like we did 200 years ago (like build houses). But even in those areas a lot of things are not round units.
When things are not nice round units though both systems are equally hard. This is common in the modern world where we do a lot of things impossible 200 years ago.
in reality you almost never calculate on the job. You measure what is on the print and anything not on the print is figured out 'when you get there' by measuring the space left when you get there - which also corrects for previous measurement errors
Units based on base 12 or base 2, as U.S. standard measures tend to be, are easier to divide in many ways.
Now if we used base 12 numbers instead of base 10, and we had a system of units based on that, I bet we’d have the best of both worlds. No idea if Napoleon could have imposed base 12 arithmetic on most of Europe the way he did metric, though.
When one of familiar with something, it always feels more natural.
No. They are only more natural to you because you are used to it.
Can you give an example? I can't imagine calculating conversions between inches and feet to be easier than using millimeters/centimeters/meters. Or using mostly millimeters in construction in Europe. You have one unit to deal with that generally tends to be integer value. No need to fractions.