Formalities, respect for your instructors, and other non-butt whupping related practices are essential to ensuring that a good training atmosphere is maintained. On top of that, they ensure that the club maintains a respectable front for visitors. On the flip side, a bunch of bowing and hop-to-it-ing that mean little in a western setting aren't going to achieve that. Informal training sessions between senior students aren't such a big issue, because hopefully, a regimen of respect and courtesy have left them capable of treating each other in a reasonable manner. There's more to MA than just turning out thugs, you should hopefully be teaching people something about being a decent human being.
The martial arts don't turn people into reasonable respectful human beings (I can name some amazing MAists of the top of my head who were complete jerks), a good learning atmosphere and a level of respect and formality within the dojo do that.
Iain Richardson, compulsive post-having cake eater-wanter.
"He shoots first who laughs last."
- Alexsandr Lebed,