There are many reasons to ride a fixed gear. Roadies have ridden fixed in winter for ages for training. Because you are limited to a single gear, you will almost always be in the wrong gear: if climbing or with a headwind, your gear will be too big, forcing you to mash, which will develop strength; if descending or with a tailwind, your gear will be too small, forcing you to spin, which will develop supplesse. Together these will widen your effective power band.