Currently, we have one 12 real world hours treated as 24 in-game hours. This is to accommodate for timezones, such that everyone can see day and night at least once in their timezone. It is also important because certain pokemon only show up at certain times of day.
The 6 and 3 hour cycles would probally happen far to quickly for it to seem belivable, particulary the 3 hour one.
The 24 hour cycle posses a slight problem in time zones. I know I personally often get ‘new’ things late due to my time zone, and i definatly dont want to be stuck with one or two times of day because of were i live.
The current 12 hour system works fine, and is probally the best.