I'm British, 72 years old (almost). I grew up under the imperial system:
12 inches = 1 foot; 3 feet = 1 yard; 22 yards = 1 chain; 10 chains = 1 furlong; 8 furlongs = 1 mile.
12 pence = 1 shilling; 20 shillings = 1 pound sterling; 21 shillings = 1 guinea.
16 ounces = 1 pound; 14 pounds = 1 stone; 8 stones = 1 hundredweight; 20 hundredweights = 1 ton.
and so on
It didn't make a lot of sense to me, and I sighed with relief when decimalisation came in. BUT... at primary school we did a lot of mental arithmetic: "what's a third of a pound - six shillings and eight pence"; "how many square feet in an acre - 43,560"; "how many fluid ounces in a barrel - 5,760". Ok, most of us needed pencil and paper for the last two, but all but a few were quite able to do this stuff at age 10.
When schools were relieved of this burden, they could have expanded teaching of literature, science, languages. Instead they seem to have filled up the time with cutting shapes out of coloured paper and finger painting. So did the more difficult system train our brains better? Probably not, otherwise American kids would be streets ahead of Europeans, which doesn't appear to be the case.
One non-SI unit I can make a case for - the temperature scale. We use Celsius, based on the freezing and boiling points of water, split into 100 steps of 1 degree. Fahrenheit used the interval between the lowest temperature he could reach, and human body temperature (he must have been running a slight fever that day). The result is a scale which covers all the temperatures we normally encounter weatherwise. That's what we mostly use temperatures for, and it's meaningful. Temperature in the 30s - icy; in the 40s - chilly; in the 50s - cool; in the 60s - warm; in the 70s - hot. With Celsius, most of the day-to-day temperatures are in the bottom third of the scale, with some leaking down to minus. Is that logical? Or is it a case, as the Americans say, "that's what we're used to, so we're sticking with it."