Watches

You could build a machine to orient them all the same, each getting the same number of turns, each leaving the head in the same orientation, etc, but even a human can do that with ease. The problem with that is that the torque on each fastener will not be the same if you do this, and it'll do a poor job of holding together the thing you've just assembled. So, you want to assemble them to the same torque to ensure the fasteners stay fastened. But, now you have two things that will prevent them being the same orientation. The first is that the tolerances of the two surfaces are not absolutely perfect. Even if they're not just good, but actually amazing for a metal component, with surfaces that are flat and parallel to 10 micron type tolerances, with small fine pitched fasteners your screw head, or your nut, as in the case of AP's assembly method, will end up with a slightly different orientation just from that. Add in the fact that the nut and bolt will wear together and distort each other as they tighten, by an amount likely greater than the amazing specs of your honed metal components you're fastening, and will do this each time you use them, and they'll definitely end up in slightly different orientations if you want equal fastening force. So, you get to choose: have your fasteners do a good, precision job of fastening, holding your components together securely as intended, or have them all perfectly aligned. Reality doesn't let you do both. AP artfully cheats a bit, aligning their bolt heads nicely, and letting the nuts take up to slack. Hublot lets their screw orientation be whatever it is, because they're screws, not nuts and bolt where you can at least choose a fixed orientation for one of the two components.

I believe you mentioned you had a Lange? Take a look at the movement. Even closely spaced screws, ones that should have minimal difference in thickness of the bridge, plate, or other component they're holding down since they're close, will have different alignments. For example, take a look at the three screws holding in a gold bearing chaton, they're all over the place, as far as orientation of the heads. This isnt because the 3/4 plate back is horribly lumpy, or the screws all have wildly different clocking of the thread lead-in relative to the head orientation, it's because they're all torqued properly, and this creates minor deformation in the faces of the threads, both on the screw and the material it's being screwed into, leading to different screw orientation. Replace those screws, and the replacement ones will end up differently oriented, too.

I'm neither a machinist nor a watchmaker, I'm a scientist, but I have spent a lot of time working on problems of how to build things far, far more precise, and far, far more expensive than a $150K watch, often things that have to work correctly and reliably for extended periods in very difficult environments, enduring mechanical shock, vibration, hard vacuum, high energy plasmas or radiation, temperatures from -150 C to 800 C, that sort of thing. It's honestly given me a lot of perspective of the challenges of precision machining and assembly and the limits of materials, and given me the opportunity to work with a lot of top notch mechanical engineers, machinists, and highly skilled assembly technicians. It's also given me a lot of appreciation for when precision machining and assembly is done well, and what should and shouldn't bother me about an assembly. Fastener orientation doesn't bother me. Fasteners which work themselves loose because they weren't properly tightened, on the other hand...