What ain't there and ought to be.

[Lalwendë]

I think the question of the absence of 'graveyards' arises for a good reason, and though what you say is a good point, it is the fact that we see a significant battle with deaths resulting that brings up the question - we expect to see graveyards/burial rites because we have already seen them in other parts of the book. Throughout LotR we see many deaths, which are usually followed with solemn 'burials' - I say 'burials' as not all are actual internments, some are more 'funeral rites'. In addition, to Hobbits, funeral rites are not a strange concept as they see these in other cultures.

Yet we do have graveyards of a kind in The Shire after the Battle of Bywater:

Nearly seventy of the ruffians lay dead on the field, and a dozen were prisoners. Nineteen hobbits were killed, and some thirty were wounded. The dead ruffians were laden on waggons and hauled off to an old sand-pit nearby and there buried: in the Battle Pit, as it was afterwards called. The fallen hobbits were laid together in a grave on the hill-side, where later a great stone was set up with a garden about it. So ended the Battle of Bywater, 1419, the last battle fought in the Shire, and the only battle since the Greenfields, 1147, away up in the Northfarthing. In consequence, though it happily cost very few lives, it has a chapter to itself in the Red book, and the names of all those who took part were made into a Roll, and learned by heart by Shire-historians. The very considerable rise in the fame and fortune of the Cottons dates from this time; but at the top of the Roll in all accounts stand the names of Captains Meriadoc and Peregrin.

What is interesting in this passage is that the communal burial with a stone and garden is highly reminiscent of the war memorials we see today. The 'Roll' also brings to mind the boards which are seen in churches listing fallen locals in various conflicts. So we do not see an extensive graveyard, but we do see that the fallen Hobbits are buried, and they do receive an appropriate memorial and resting place.

Another interesting aspect to this is that in the fourth version of A Long-Expected Party it is said of Bilbo's death (as was intended at that time):

His relatives and neighbours lost the chance of a funeral, and they had a good deal to say.