Actually, I think all bikes should have front and rear brakes, fixed or not.
As the resident brake Nazi I have to disagree... of my five fixed gear bikes only one has dual brakes because it is used for loaded touring.
When it comes to SS bikes, I feel that they definitely need two brakes as do coaster equipped bikes so that their braking capabilities are maximized.
You can generate maximum stopping power with your front brake and a rear brake or a fixed drive allows you to modulate speed in conditions where applying the front brake can be hazardous such as during high speed turns and less than ideal road conditions.
I have one coater only equipped bike (made in 1933) that has no provision to use a front brake and I ride it accordingly knowing that my stopping power is less than half of what it would be with a front brake. I allow for greater stopping distances and will only open it up on stretches where having to make panic stops are unlikely.