I did some experimenting and found that (at least in SU 2021 on Mac) in Architectural Units, things such as dimensions never show the ~ when feet are present, regardless of whether the inches are imprecise or rounded. With 1/2" precision set, you will get a display of 1’ 1/2" for anything in the range 1’ 1/4" to 1’ 47/64" (1/64" less than 1’ 3/4"). In this screenshot, one edge is exactly 1’ 1/4" and the other is exactly 1’ 47/64". Neither is 1’ 1/2"!

You can form your own opinion whether this is a bug or intentional, but if intentional the training certainly should point it out!

Edit: I didn’t go poking to find out how close to 1/4" would round up to 1/2" or below 3/4" would not round down. It seemed the point was made.

Edit 2: Here’s an amended screenshot that shows how absurd drawings can result: