I seem to remember playing with the graves hoping to push them back and get money or find some secret lair. I mean, grave-robbing is Zelda tradition!
I'm definitely for the idea of being able to read the graves. I was dissapointed at not being able to do that in Twilight Princess, too. You see, in real life, I live across the street from a cemetary. I do not know anyone buried there, but I like taking walks and reading the stuff on the headstones - names, dates, bits of poetry. I mean, there are graves from the 1840s there as well as recent stones. You can get a sense of history in a graveyard - and history is important in Hyrule and related lands...
In my head-canon for the Skyloft Graveyard... I don't think anyone is actually buried there, for at least very few people - maybe ashes, because the area is not very big, nor is the ground very deep. I'd think on a sky-island, land would be at a premium, therefore funeral that take up a minium of space would be popular. I created a popular funeral rite for Skyloft for my fanfictions, it's been mentioned in a couple of them: "Sky Burial" via Loftwing. The deceased is placed upon a scaffold and taken away by their Loftwing. If you want details, I can link you to my fictional Loftwing guidebook, or to the chapter of a story-fanfic in which I had this done to a popular character. I think the graves are likely records of family-names of people who died, a marker for every prominent family/clan.
Still, I think it would have been nice to "grave-rob" or to hunt Poes, or to meet the friendly spirit of a fallen Skyloftian (Pipit's father, pehraps), who has friendly advice and/or gossip about the people of the island.