I have a custom frameset in the works, and the frame-builder has shown me that I cannot have a front brake with the type of fork I want; and so, I must decide between the fork I want and a front brake.
I have ridden fixed for four going on five years, now, and in the past year I have used my front brake perhaps twice, and not necessarily because I needed to use my front brake but possibly because I had one.
I ride SPD clipless, and I think I might only need a front brake if I inadvertently unclipped at a bad moment.
In other words, if I could guarantee that I would never inadvertently unclip, I would go with no front brake without any further thought.
Now, I can do several things to minimize the probability of unclipping at the worst possible moment.
First, I can maintain my pedals and keep them perfectly adjusted.
Secondly, I can continue my practice of not going downhill as fast as I possibly can, but, rather, as fast as I can go with complete control.
Thirdly (and the reason for this discussion), I can switch to clips and straps.
I say this, regarding clips and straps, because my son rides his geared bike and his single-speed with clips and straps, and he reports clips and straps as more secure than SPD's (and as functional), but only because he tightens his straps as he rides.
I don't see any way I could tighten and loosen my straps riding fixed (I did so years ago on my geared bike), which means riding with the straps loose enough to slide my foot in and out.
This ability to slide my foot in and out would mean I would have to adjust my spin, and, in the end, have a less efficient spin.
See the issue?
So, I don't intend this as a brakes or no-brakes debate, but as a discussion of brakes and no-brakes from the perspective of spin and foot-pedal connection.
I don't expect an answer from the forum, but I think a discussion might help me make my own decision.
Right now I lean towards no brake, well-maintained SPD pedals, and riding more conservatively.