This is the short answer (in Mormon speak): Because I have a testimony of our responsibility as stewards of God’s Creation.
Elder Oaks gave a great talk entitled Good, Better, Best. Some might put sustainability into the "good" category. I confess that when compared to the things of eternity, temporal issues like sustainability may not fall in the category of "best" or even "better." However, I would point out that Earth is spiritual as well as temporal (Moses 3:5), and that the Lord saw fit to dedicate small portions of the Scriptures for instruction on environmental stewardship issues. Thus, I am content to hope that Latter-Day Sustainability will fill a small, if only "good" niche.
Clearly there’s some religious significance to the good-better-best business that’s going right over my head. But hey: the more the merrier.