Shoes are an important piece of riding equipment. For Downhill, slalom, jumping, etc, there are two points of contact attaching you to the bike- Hands and feet. For XC or all mountain, there is the seat seat as well, but yeah, hands and feet are still the main contact points.
One of the main reason's why 5.10 has dominated in Downhill with the Minnaar and Hellcat models, is because in gravity racing there are a lot of different loads on your feet. You turn, jump, land sideways, pump etc. Having a good feel on the pedal with a slightly flexible, comfortable, yet protective shoe is ideal. For road riding and even xc racing to an extent, most of the pedal force is linear, so having a carbon sole, or really stiff shoe makes sense. In BMX you need to transfer everything you have directly down through the pedal, but the skill and movement still come into play, light rotational weight is key as well.
Five ten rubber is hands down the best for flat pedal riding. It absorbs vibration, grips the pedal like no other, and is thick and protective in the sole. Everyone should mix it up and ride flats and clips to see the difference. Almost all our skills days are on flat pedals because flats are fun to mess around on, easy to correct mistakes, and help expose where your natural foot position is. On DH trails that are really steep and Muddy, I practice flat pedal riding as it helps with basic fundamentals of timing and hopping over stuff. Plus if you get sideways, it's rad.
We get asked which shoes to use all the time. So my recommendation is to ride the lighter Maltese falcons for trail riding, Minnaars / Hellcat or Impacts low for dh, and freeriders for skills and jumping. enjoy:)