Here's a thought. The Shire was a very peaceable land. No wars, no need for town walls(exception: Buckland's Hedge) or armies or a large police force or anything like that(which could be another ain't but ought to be: army/police). The biggest problems would probably be tavern brawls, which I imagine there would be quite a few, considering how much hobbits drink.
But seriously, the Shire was very quiet and peaceful. Maybe Tolkien put the graveyards
out of the picture because it would
ruin the picture. Really, cemeteries are very scary places, especially in Middle Earth. I can certainly see why it would make the Shire seem less... well... Shirelike. It might make it more real, but it would ruin the quiet and perfectly peaceful feeling.