I was thinking that if shipped in a bubble mailer, the case gets pressed on in transit, which would increase the likelihood of the disc coming loose. If shipped in a box, the case does not get pressed on.
Also, it's not my job to re-set the disc of a brand-new game I paid full price for. If I try, the chance of me cracking the case or scratching the disc more or ruining the factory wrap is pretty high.
1) LRG has numerous ways to address this the best they can on their end being that it's Sony's problem, not theirs. You can pay for a box or you can order 2+ games with at least one being a PS4 game and get a box automatically
2) Sony is the party at fault for loose discs. The case design sucks. Nothing anyone outside of Sony can do about it.
3) Given that the non loose disc requirement is your own stringent requirement, in the face of #2 you are forced to accept this is unrealistic and then decide how you personally will address it. You can get good at reseating loose discs so its no longer an issue, buy multiple copies to improve chances of getting a non-floater, meet the requirements to ship games in a box to minimize the chance, etc.
I hate loose discs too. I've been collecting every PS4 physical US release since day one and deal with loose discs daily. I used to exchange them at a local store even until I learned how to reseat them. I was able to perfect numerous methods of effortlessly reseating them without damage to the factory wrapping or case.
Practice with a disposable sports game or something that's already open and practice and experiment with the interaction between the disc and the hub until you perfect it. The method shown in the video is best as it puts both necessary downward force on the disc and also allows it to slide a bit to hook over the opposite side after anchoring the near side. If you do this slowly with an open case you'll see what I mean. Works every time.
But still, if you have this asinine requirement, as I do, then you have to at least accept the fact that it's nobody's fault except Sony and they don't appear to be addressing it any time soon, and deal with it somehow.
Very rarely I'll still exchange games that have no chance in hell at reseating on the grounds that 1) the case is broken, eg: piece of cracked off plastic rattling around inside 2) one of the 3 prongs was mashed at the failed factory attempt to press the disc in and is also effectively a broken case. Both can be easily observed with a 1000 lumen flashlight. This only applies for normal retail outlets and obviously differs with LRG, which is why when it comes to LRG, iam8bit, fangamer, and other limited releases that I'll never have a chance to replace or exchange, it's one of many reasons I always pick up 2.