The country would be a better place if more people did.
Supreme court decisions are phenomenally well written. They usually begin with a clear, short, and accessible statement of the case and the relevant principle(s) before they summarize their decision. I find that they describe the issues surrounding the cases with great compassion for all the major arguments. And the dissents are usually equally informative.
Reading decisions has dramatically increased my appreciation of the nuance that goes into the decisions of the court and the operation of our country. Even for cases where I disagreed with the judgement with both before and after reading the decision, I gained a much greater perspective of alternative views. ... and a feeling that even when I strongly believe we're doing the wrong thing that we're trying so hard to do the right thing that eventually we'll get it right somehow.
For several years I read at least the beginning of every decision and dissent -- there aren't that many. I stopped only because I became crunched for time, and I'm thankful that your post reminded me of this gap from my life now that I have the time to pick up the practice again.