A relative of mine wasn't much into gift wrapping. As a matter of fact, sometimes she'd come with a bag full of Christmas presents and ask me to wrap them for her because she knew I enjoyed doing it. Why bother with wrapping a present? The short answer is to make magic. The long answer goes something like this. Although we suppress our childlike enthusiasm later in life too often we love surprises (that's for the recipient) and we like to play (that's for the giver who gets to wrap), and we also enjoy watching the look of joy and surprise on the recipient's face. Besides, most of us enjoy beautiful things.
I think a beautifully wrapped present increases in its inherent value manyfold. A little trinket can become downright precious with the right wrapping. I guess I shouldn't say this too loudly - but I oftentimes buy relatively inexpensive presents (quality of course, no junk! perhaps something on sale, perhaps something small, perhaps a homemade food item) and make it look really special and precious with creative gift wrapping. It's the thought and the intent behind the gift that counts more than what the item's price tag is.
The Japanese - who have a very well developed sense of aesthetics - have perfected the art of gift wrapping. One way is to wrap presents in cloth, that art is called furoshiki. They also have a special way with paper, called tsutsumi.
When Christmas comes around and I need to wrap lots and lots of presents I make a special event out of it for myself; some Christmas music, all of the paper, ribbons, gift tags and accessories spread on the floor and table, a cup of tea or a glass of wine - and then I create and wrap. I get to play and make it all look beautiful, and the recipient gets eye candy. It's another quality of life idea. Enjoyment all around.