"A fixed-gear bike with no brakes cannot stop in as short a space as one with a front brake, because only the rear wheel is providing the braking force. As a vehicle on the road, it's therefore clearly less safe.
This is a matter of simple physics. In the third edition of Bicycling Science, David Gordon Wilson demonstrates that the maximum deceleration of a crouched rider on a standard bike (that is, not a recumbent) on a dry road is 0.56g. Try to brake any harder than that and you go over the handlebars, which is the limit condition, as the limit from tyre adhesion of vehicles that don't pitch over (tandems, recumbents and cars) is about 0.8g.
If you brake with only the rear wheel, according to Wilson, the limit is 0.256g, because braking effectively shifts your weight forward, reducing the load on the rear wheel to the point that it skids at that deceleration. Once a tyre is skidding, its braking effectiveness is reduced because you no longer have sticky solid rubber in contact with the road, but a lubricating layer of molten rubber."