In some parts of the northeast, and I'm sure other inland locations with vis that we typically get, the difference between the octo up on the chest and down on the hip can be the difference between finding it and not finding it. On the hip I have seen numerous divers enter the water blissfully unaware that it has become dislodged and is now trailing behind them. Not what you want to have happen in a stressful situation. On crowded boats you are also risking someone setting their tank on it and damaging it.
For my classes it's not enough that you and your buddy know where it's at. Anyone should be able to easily locate it. That means the one or two weekend wonder who was not taught gas management and is now coming at you wide eyed with both hands grabbing for your reg or your octo should at least be able to see it. Whether they go for it or the one in your mouth is a 50/50 proposition. If it's down on your hip pretty much assured they won't even glimpse it.
As regards the earlier point about it coming loose. If your octo is that secure that you're not really concerned about that, it's possibly too secure and may delay deployment. I use nothing but surgical tubing and zip ties for octo holders. Cheap, easy to replace, not likely to grow legs as some of the commercial ones on shop BC's seem to do from time to time, and they don't restrict deployment in any way.
Clips on the hose, things that jam in the octo mouthpiece, etc. are less desirable.