It has always bugged me that the world operates on a roughly 9am-5pm schedule, but it has been bugging me more lately since I have transitioned from shift work to an all day schedule. Sure, it's nice having a normal sleep pattern. However, it was nice being able to shop in off-hours when there's nobody else around. One major inconvenience is the hours of the post office here in Girdwood. Because I commute and I'm not home from work until about 530pm on weekdays, the post office is already closed. Therefore, the only time of the week I can pick up/send packages is from 1000am-noon on Saturday, which isn't terribly convenient either since I like sleeping in on Saturday.
Since weather doesn't take a break at night, meteorologists with the National Weather Service work 24/7, of which I am very proud. I often wonder if the world would function better if it ran on a 24 hour clock. Some benefits include the lack of rush hour traffic, being able to shop any old time, and being able to play a round of golf on Sunday without ridiculous crowds. A drawback would be not being able to coordinate with all your coworkers (like we experience at the National Weather Service). Strange sleep patterns wouldn't be a problem with a 24/7 society as long as those who work nights work nights consistently, and those who work days work days consistently.
The change to a 24/7 society would have to occur in pretty much all aspects of society for it to be truly effective. However, I think we are headed in this direction. For example, even for those who work 9-5, it is common to check and respond to email through the evening, or even during a bathroom break in the middle of the night. Also, more people are telecommuting in an increasingly global society. There are probably a lot more benefits and drawbacks to a 24/7 society than I have mentioned here. I doubt it will ever happen completely, but I can dream.