I would suggest that one of the major reasons that US still uses Standard measurements in engineering has to do with "network effects" that date to the two world wars. During the second world war, European factories were heavily bombed and after the war they needed to be re-tooled. In contrast, American industry tooled up for the war, (using standard measurements) but was never bombed, leaving a surplus of high quality tools, many of which are still serviceable to this day. When you are making a new mill or lathe, it doesn't really matter whether it is calibrated in standard or metric, but re-calibrating an existing machine for a different system of units is very costly.
On a typical manual mill, for example, turning the traverse handwheel a complete revolution moves the table by an integer number of thousandths of an inch (usually 100 or 200, which are 2.54 and 5.08 mm). To operate the mill in metric units requires either that the operator remember that a revolution is 2540 micrometers (awkward) or rebuild a significant precision part of the machine (the leadscrews and leadscrew nuts). You might think that this wouldn't be a problem with CNC mills, but many use stepper motors to turn the leadscrews. Those stepper motors might have only 200 or 400 steps per revolution (giving a resolution of 1 to 0.25 mils, or 0.0254 mm to 0.00635 mm) which can make it inconvenient to use metric units.
If that weren't bad enough, collets (basically an adapter to hold the "bit" in the mill) come in standard sizes to hold mills (what you call a mill "bit" used on a milling machine. yes, it is confusing) of standard sizes, which are typically fractions of an inch on US equipment. When you are machining a piece of metal, the finite diameter of the mill it usually important. The accessories that go with a milling machine can easily add up to more than the cost of the machine itself. So, to really operate a mill in metric units in a convenient way, you'd also need re-purchase all the little parts that go with the mill.
Someone is probably going to reply that these issues don't apply to modern CNC tools. I'm not familiar with those, but the point is that there are a significant number inexpensive and serviceable tools in the US that can only work with metric units in a very awkward way (or at great expense).