Waaay back in the day when I was a hard core bike racer, before there was anything hip about it, I converted an old road bike to a fixie. The point of riding one was that it helps, vastly, with helping you learn how to spin and eliminate the "dead spots" in your pedaling. It was a fairly common winter training machine amongst the boulder racing folks I hung with. A fixie is non forgiving: you cannot coast, and wherever you are not exerting effort while pedaling you notice immediately. Riding one for months on end means when you get back on your road bike your legs have the muscle memory that allows you to pedal at a high cadence for a long period with very little fatigue, which is a great benefit when you are racing crits week in and week out.

As long as there is a front brake, there is nothing dangerous about it, unless in a moment of non-mindful pedaling you forget that you cannot coast. Kind of the same surge of adrenalin as when you forget to pedal for a moment (or brake!) on rollers. If you are skilled rider, there is not much dangerous about it at all, even with no brakes, unless you need to stop suddenly. There are tons of big city messengers who ride brakeless fixies, as they know how to.

Also, most fixies and track bikes are very different animals as far as geometry is concerned. A lot of track bikes become fixies for lack of actual track riding, but a fixie can be any bike set up with a non-freewheeling cog in the rear.