Kind of amusing to see folks defending riding without brakes while claiming that riding without foot retention is extraordinarily dangerous.
To the OP: there are almost no practical advantages to fixed over free. There's a reason fixed was abandoned by road racers more than fifty years ago: freewheels and multiple gears are better - in practical terms - in almost every situation. The reasons that some people still choose fixed are these:
1) Riding a very small (<65 inches) fixed gear can improve your pedal stroke. (Larger gears can actually make it worse, as they allow you to let the bike propel your legs through the dead parts of the stroke.)
2) A fixed gear bike can be among the simplest bikes available. Some people appreciate that and are willing to compromise in other areas to get it.
3) A fixed gear is historically correct. If you want to know what it was like in the Tour de France before 1936, for instance, get a comfortable FG bike WITH BRAKES and go ride it on your local dirt roads.
4) Some people simply like the way a fixed gear bike feels. That doesn't have to be rationalized and probably shouldn't be.
And of course, the single most popular reason these days:
5) A fixed gear is necessary if you want to be one of the identical individualists currently perpetuating the fixed gear fad.
HTH!