If you ride fix gear very fast downhill. good toeclips, straps and cleats give you the security of knowing that even if cleat releases, your feet are still on the pedals. I find that at pedal RPMs over 175 I have a hard time being aware of whether I am keeping my feet straight (especially when I am offsetting my weight for a turn. (Cars have told me I was going 45 when I was riding a 44-17, 215 RPM. Years ago, I used to go a lot faster on a 42-17.)

Toestraps pulled tight give you the freedom to ride and never think about your pedals, no matter how fast or hairy the going gets. (You do have to remember to loosen them before stopping, but the worst that can happen is you fall over at very low speed, not have your ankle struck by a heavily weighted hammer swinging at 200 RPM. That "hammer" isn't light. It effectively weighs you + the bike times the gear ratio you are riding times the difference between your wheel radius and your crank length. Say 150 lb rider + 20 lb bike X 42/17 X (27/2)/7 = 810 lbs. Makes a sledge hammer look like a toy.)

Edit: Exustar maks a good road cleat for quill/rattrap pedals. They call it a track cleat, but it is what we would have used 40 years ago before clipless had modern shoes with bolted cleats existed then. They require the LOOK three bolt shoes (although they only use the rear two bolts). Cost is about $20. These are very high quality cleats. Don't get the $75 model. THose are track specific and for the incredibly strong sprinters who care far more about having a cleat that will reisit the hardest pull up than whether they can actually get their foot out when they stop. (They always have a rail they can pull up to grab.) If they won the race but it take 5 minutes to get their foot out, cool! The cleats worked! Obviously not what you want in traffic.

Ben