That's the drawback of living in a country where things are so plentiful. Think of other things you throw away: the tops of carrots, citrus rind, potato peels, corn cobs and more--all of which could be used as ingredients in delicious food.
Leaves of carrots, celery and fennel can be used to flavor sauces or as herbs in a salad. Many "scraps", like corn cobs or the woody parts of asparagus, can be used to flavor stocks. Melon rinds can be pickled or even used raw in a salad. There are limitless uses for the things we throw away.
Using up these kinds of ingredients may take a little research and a little more time, but we should take a cue from cuisines of other countries, where using every possible part of a plant or animal is commonplace--and necessary.
An interesting and informative article from the New York Times tells about the ways that chefs and others use these kinds of ingredients to save money and eliminate waste. Maybe it'll help to inspire us to use food for all it's worth!