The clack seems to be a bushing problem but not sure what it is about the bushings that cause it. It's funny to think there are multiple factories I guess arcade stuff is still pretty popular
Did you try lubing the socket?
It's not as simple as "multiple factories", and that may not even be true. Injection molded parts come from multi-cavity molds. Each cavity is slightly different, and the molten plastic flows into the cavities at different points during the "shot". There will also be minor variations in temperature and other aspects of the run. While injection molded parts are pretty uniform, given the cost per part, they are not going to be absolutely perfect from one part to the next.
I have a couple dozen of these sticks here, all from the same place (HAPP) and managed to find one that clicked a bit. The others didn't. I put some lube on the socket, and the click went away. You are also dealing with a part subject to some pretty heavy friction. This means that the dynamic will change once the part starts to wear a bit from use. Not so different from breaking in a trackball, which mates the ball to the roller, and seats the ball bearings to the internal races.
If you use the stick for a couple of weeks,
after you've taken any simple steps (like lube) to mitigate a perceived issue, and it continues to persist, then feel free to obsess about design / manufacturing aspects. At this point in the overall process, however, it's somewhat pointless. Sort of like spending time analyzing the weight, grip material and balance of a hammer before you try pounding a nail.