I just acquired my first ss/fixed biked (currently running it fixed with front brake). I had a few reasons for acquiring this. I live in a metro area.
1.) Simply popping out on the bike to run quick errands or head to a bar a bit longer than I feel like walking to, when I don't want to drive, and in lieu of uber is great. That said, I won't lock up and leave my road bike. I wanted something simple and cheap that I wouldn't care (as much) if it were stolen.
2.) Theft aside, I've briefly locked up one of my carbon bikes in the past at the end of a rack. During the 15 minutes it was locked up someone roughly locked up their cheap walmart machine next to it. My paint/clear coat was badly chipped and rear mechanical was bent out of alignment. The later point furthering my decision to go ss/fixed. No one else carelessness will result in dirty hands or lost time.
3.) Improve my pedal stroke/spinning skills. Over the past 2 winters I started riding rollers during the winter. It's made a noticeable difference in the way I ride. I'm sure fixed will further refine this area of my riding by default.
4.) To be honest: Curiosity. I wanted to see what all the hype was about. It's been really interesting and actually I do like it a lot. I'm still undecided at this point if I will keep this bike as fixed or ss. I need to get some more saddle time on this bike before the decision is made. Busy season at work and more or less daily road rides have been eating up my time and energy.