Simplicity.
I don't believe there's enough difference between the simplicity of a fixed cog over freewheel to even consider it a benefit. Replacing your freewheel once every two or three years isn't a big deal.

Traction/control/feedback
I think the ability to adjust your speed without a brake is an small advantage. Making little speed adjustments without having to reach for your brake can be nice, particularly when moving slowly. I think the whole feedback thing is just a little overrated. I can feel instantly when my back wheel is loosing traction on a coasty bike both while pedaling and braking. Any good cyclist is in tune enough with the bike to know what it feels like when the rear wheel begins to skid no matter what the drive train. You can modulate a brake much better and apply more even pressure with it than you can with your legs. The only major advantage fixed gear has here is when your brakes/rims ice up, but again it isn't a huge factor most of the time, even when it's snowy and icy.

Trackstanding
This is the single best thing about fixed. Trackstanding is harder on a coasty bike, but you can do it in most situations, so this isn't a super huge advantage for FG.

Pedal strike, bunny hopping, chain issues etc...
Being able to coast is a big advantage in many situations. Getting something caught in the chain is not a big deal at all on a coasty. Having a chain come off and get stuck isn't a problem either. Both of those things can be serious problems on a fixed gear.

From a practical stand point, that is, if you ignore fun, zen and image, there just isn't much that makes a FG better. The ability to coast outweighs all the small advantages of FG. I'd still much rather ride a fixed gear, it isn't all about being practical.