You get first shot at the water, you choose where to go and when you want to leave, and your day won't be ruined by being out-fished (common occurrence around here).
Fishing buddies are good to have and important, but not just anyone with a fly rod will do. Most of us who fish hard are somewhat selective regarding with whom we will fish. I have an outstanding group of fishing buddies, but when they're busy - that's cool too.
One problem, however, is that you usually don't get the photos you'd like (see below). It's often the fish-on-the rocks-compared-to-the-net or -rod, or just the fish's head, or the fish in your hand as it droops away from the camera.