My answer includes a lot of speculation on the specific decisions of the movie makers, but I have studied book-to-film adaptation at university so hopefully I am on the right lines and I don't believe there are quotes out there on this film-making decision.
It's mostly to do with (as in most adaptation changes) A: timing
and B: the fact it's a visual medium.
In the film's penultimate scene on the bridge, a lot is dealt with. Harry is able to show the audience that he doesn't want the Elder Wand for selfish reasons and make sure that no one else will use it. This is essentially the same meaning as in the book, but simpler for audiences and quicker to show. Keep in mind that the book was already made into two films (which was actually fairly rare at the time) and still both are fairly long.
Also, in the book, we are able to learn some of the things that Dumbledore felt about the wand and the Hallows such as his very personal desire to have them but his struggling with his own history on the matter. He decides that he is "fit only to possess the meanest of them, the least extraordinary [the wand]" and so in the book there is a clearer understanding of why Dumbledore had the wand, where he got it from and his fairly complex relationship with it. In that context, it makes more sense for Harry to respectfully return it to his headmaster. In the films there isn't much time for this, film-only viewers might be thinking "OK, so Dumbledore had the special wand, that explains some of his power. OK. Move on." And they are swept 'on' by a film focused on pacing.
As for the visual medium thing... It's absolutely fine for JK Rowling to describe that Harry returned the wand to Dumbledore's grave in a few sentences. It works. You imagine it and you think that it's pretty fitting. He also fixes his wand with it, which is the aspect of this that I kind of wish they did show.
But the movies would have to create a whole extra scene showing Harry going to Dumbledore's grave and opening it up. In the way they actually did it, as I said above, the essential meaning is preserved but the scene is quicker and the idea of Harry getting rid of the wand and preventing others from using it is presented in a less emotional, complex manner.
But my main point in this paragraph is this: Do Warner Brothers really want their audience to SEE Harry Potter open up Dumbledore's grave, for any reason? It's one thing for Voldemort to do it, and that scene is built around his complete disrespect for his adversary. I know Harry would do it very differently, and they'd carefully shoot it that way, but it just wouldn't LOOK right for Harry to do it. It would surely upset some parents (though probably not their kids in my experience!)
In summary, I think it's purely down to the adaptation process. Keep the overall meaning the same, but changes must be made when moving from one medium to a different one.