I am not sure if this fully answers your questions, but one of the places where unit conversions happens a lot when doing customary unit engineering calculations is dealing with various constants/properties. For example, you might get the specific heat capacity of some material in terms of gallons, but you're dealing with ounces of fluid, and so you stick a conversion in there. It's certainly kind of niche, but it's really annoying to deal with.

But agreed on the half-assed metrification. I'm from Canada. I still buy pop and beer in 355ml cans, 591ml coke bottles, 600ml pepsi bottles, and 2L big bottles. My wood is still sized in inches (or nominal inches).

(I fully support SI though. In theory, I no longer need to memorize a whole set of conversion constants. In practice, I live in Canada, so I still need them).