As a person who has many, many hobbies, these are my reasons:
1. God gives us sacks of Gold. Are we to bury them in the ground because we don't see the use, or are we going to multiply and multiply these sacks of Gold and be entrusted with new ones?
I'll tell you something I just found out: you can learn talents that you never had before if you are faithful with one's you already had.
2. Hobbies are a sort of relaxed fun way to learn tools that you can later use for God's glory. Example: I do ballet. There was one ballet movement I just couldn't get. My teacher spent 1 hour of her own free time trying coach me and I just couldn't succeed. I spent a whole month, stubbornly try to figure it out. Rather than doing a sloppy job and pretend I was as good as the average ballet student in that class, I made a fool of myself, doing a simplified beginner's version of the exercise. Stubbornness was what I used. And one day, like magic, I suddenly and instantaneously learned how to do it in 5 minutes. This experience has been to me one of the most encouraging things. It taught me how to learn things I don't have a natural knack for. I can apply it to any other field. So that's a way to be more useful to God.
3. Part of the recipe that makes geniuses, is being encouraged into a wide range of hobbies and areas of interest when you are young. (The other ingredients are: specializing as you get older, having a mentor, and working on the specialized area 3 times more than the average amateur.) Even if you weren't encouraged as a child, it's never too late. Why not jump to the chance to make yourself as smart as possible for God's use?
4. Keeping lucid and young. An 80 year old friend of mine is one of the funnest, most interesting people around. Unlike most people his age, he is so modern. He has lot's of hobbies, and this in addition to his engineer career. One day I was painting, and he was beside me. I asked him if he painted. He said that he used to do it, but that if he wanted to stay young in his head, he preferred to learn something he's never done before, rather than do something he already knows how to do. A few years ago, for example, he and a friend got into making weaving machines, weaving, and dying cloth. Strange hobby, but in all his 80 years he had never done it before.
5. Loving others: This same 80 year old friend ran a film club in which he would teach how to make films. Teaching was just an excuse to be able to help younger generations and mentor them. Mentoring is a way to show love. (Remember, it's one of the ingredients towards being a genius!)
So hobbies are very useful, for our survival, and for being able to serve God better.
Even more passive hobbies are useful: for example, reading is needed if you are going to be able to do any good writing. Collecting stamps might teach about different countries and cultures. Building models teaches creative manual skills.