I think that people grief to get resources so they can build their own personal things. I can understand why they'd do it, but griefing is still very wrong nonetheless.
I would mostly disagree. There seems to be two kinds of grief. The first is to obtain resources that one is too lazy to obtain on their own and the second is for purely destructive reasons.
My experience with the first kind has been very limited aside from stolen gold blocks and other miscellaneous blocks that would be considered more rare or more valuable. The griefer comes in, takes the blocks they want and off they go. If the theft happens to cause some destruction or chaos then so be it, they got what they wanted.
The second type of grief is more prevalent. Putting holes in walls, tearing up manicured paths, placing water down. This type serves no purpose other than to amuse the griefer. With the exception of that Anubis statue, anything I have built in the mining world has been made from common materials like wood, logs, stone, or cobble. All that stuff is right there close by for the taking. Would someone really need to destroy a gravel path for the gravel resource? I throw that stuff away. The only reason I made a path in the first place was to use up all that useless gravel.
It is interesting that in that statue not one piece of obsidian was taken, which is a harder resource to come by. Presumably because it takes to much time to break. The time / destruction ratio is too high to make it worth it. But the glass holding back the water, which doesn't even drop a resource without weilding silk touch, was one of the first things to be broken, and was repeatedly broken. That along with the sandstone containing the pools. Both things have a much lower time / destruction ratio.
I don't believe the majority of grief is players harvesting resources. I think the acts are very similar to when someone finds an abandoned house or a house that is unoccupied for an extended period of time and they proceed to vandalize it. There is no respect for what is not theirs and they don't consider the consequences, there is nobody home after all, but the rush of destruction takes hold.
I like to see how long my builds can live in that kind of environment and if I continually repair them will that have any effect? I built a large head once and occasionally I would find several blocks griefed and I would repair them and go on my way. That went on for about 2 weeks until one day someone put up a sign that said "please do not grief the awesome" and the very next day someone destroyed the whole thing, completely gone, all that was left was that sign.