"Happy New Year"

So, as I was leaving a parking garage the other day and I wished the parking attendant a "Happy New Year" it occured to me, why do we say that? I mean it isn't as if some massively different thing happens at midnight on December 31st (other than most of the country being rip-roaring drunk and a very expensive crystal ball sliding down a pole). I mean, why "Happy New Year". I will acknowledge that it is a nice sentiment to wish people. But, then, why do we limit it to just the new year. On February 1st, why don't we wish people "Happy New Month"? And, on Mondays, why don't we wish people "Happy New Week"? Why does the sentiment of a happy new time period only apply to years? I think we should all wish everyone a Happy New Month starting at the beginning of every month this year and see if it catches on. Who's game?