Yes - it sounds like there are some with genuinely loose mirrors that need to be fixed. But I think in other cases people may not be re-focusing in a manner to load against gravity. And the OP is apparently collimating with the scope horizontal - which reduces the loading provided by gravity.
I'm just not sure how common this issue of loose mirrors is - because there are many of us who don't have the issue - and with multiple sct's. And a key point is that even if it is the case, it isn't a flaw in the design - but an error in assembly that apparently can be fixed.
Just to clarify, I didn't intentionally collimate it on one side. Before I realized that the mirror was flopping, I collimated on a star where it was upright. But once the retaining ring was snugged up, collimation shifted to being best on one side. Since I was interested in establishing the magnitude of the effects of the flop, I left it there. Before I tightened the ring, I found that the flop was causing noticeable mis-collimation at other angles, but not as severe as with the side-to-side flip after tightening. In-focus bright stars were clearly not round, but not horrible.
The other significant problem was that the flop shift was making it impossible to build a good model with the mount. Pointing was off by more than half a degree in some cases. When a goto mount can't even hit a target the size of the moon, it's pretty much useless. With a 6" f9 refractor on the same mount, pointing is within 3' and often within 1'.
This OTA is 18 years old. If it has been this way since it was made, then one has to wonder about how it was used. The previous owner (who works on telescopes professionally) bought it from the original owner a couple of years ago, de-forked it, replaced the tube with carbon fiber (chipping the corrector in the process), and then sold it because he felt it was too big, and because his Celestron GEM mount had turned out to be defective, and he was tired of dealing with it. He assured me that there was no issue with mirror flop when he had it, and that the mirror seemed properly attached to the cell when he had it apart. But the fact that the mount wasn't working raises questions about whether he mis-diagnosed the problem.
I suspect there are a fair number of scopes that are gathering dust because their owners don't know how to diagnose the source of poor images in them. Those eventually get sold, with claims of being "like new" because they have "only been used a few times." In some cases, it may just be bad collimation, but others may have manufacturing defects that then get passed around until they are disposed of or someone takes the time to do a careful diagnosis, and then can't resell it in good faith.
One would think that Celestron would use better quality control on their flagship optics, but there are other threads (John H. had one in particular) where it seems that even with the C14 Edge-HD, the RTV application can sometimes be faulty.
I'm not set up to pull the mirror from its mount and properly remount it, so the only solution may be to send it to Celestron. But they won't give any kind of estimate (other than for cleaning and collimation) or assurances that it is repairable, until they inspect it, so it's not clear whether it's just throwing good money after bad to send it in, or if it would be better to part it out and try to recoup some of the loss without pawning the problem off on someone else.