Note, fixed <> fixie (well it doesn't have to be)
I ride fixed a lot. Front and rear deep drop brakes (for mudguard clearance), no skidding, just treat it like an ordinary road bike. You will clip in first time about 90% of the time. I don't find that riding fixed is any different to freewheel - coasting is a pernicious habit anyway. When you start, you will be "told" that you are riding fixed at the first corner when you try and coast. Second time will "remind" you. There won't be a third time.
Start on a 42x16 or 48x18 gearing (they are the same). This is low enough for getting started at traffic lights and fast enough to keep up. It is also standard gearing on most off the shelf bikes. Anticipation is really no different to riding clipless, you will be planning when to unclip, and watching when you will need to stop. You can always soft pedal as you slow down with the brakes.
I ride our winter medium club rides at a 19-20 mph average on fixed 48x16. When I race, my average cadence on a freewheel is 95-100 rpm. These are not unconnected. I also raced the track bike IG Nocturn brakeless (see above route) and that was terrifying!
What are these "fabled benefits" that so much outweigh your safety?
You will learn to spin like a god.
You will learn to anticipate traffic conditions better.
You gain fitness as you can't coast downhill or downshift to make it easier.
You ride smoothly, and this translates to geared bikes.
You can accelerate and decelerate via pedal pressure.
You will never feel so in tune with a bike.