I love Strava as a training tool. It's a great way to track my mileage and progress, and pushing myself on segments just adds to the ride. When I don't feel like pushing or riding fast, the app doesn't kep me from enjoying a nice afternoon of meandering, but it does let me have a handy map for the next time i want to ride that route.

Crux of the matter: Nobody can make you obsess on competition or the other guys. If that takes the fun out of riding, for you, then don't focus on those things, regardless of whether you use Strava, MR, or any sort of computer.