Why doesn't the villagers bury the dead, if the game isn't open?

If they did that, then the only way you would know that villagers had died would be to check the graveyard (and remember or write down the villagers that were already there) or check the game log every time you opened the game. I like having the burials after the game is running, so I know who died.

It is kind of gross and sad to see those skeletons lying there in the morning though.

it is even grosser and frustrating trying to get the villagers to bury them... they walk over them, around them, and at times when trying to encourage them to pick them up and bury them one sees the message about their being the same gender.. not trying to promote necrophelia, just trying to get them buried..

any hints at how to best encourage burying?

It seeems that almost all the elderly villagers decide to bury the dead. The younger ones tend to ignore them. When there's only a few villagers to bury, the elderly villagers tend to arrive far too late because they walk so slowly.