Ok. I don't know how this all fits in but according to my running coach, podiatrist, and a running book I read, everone has their own specific foot mechanics. Some people naturally "heel strike" some "midsrike" and some naturally run on their toes. Whatever way you run naturally, this IS the most efficient way for you. Trying to change the movement may result in injury. the only exception would be for people who are extreme heel strikers to the point that it loses some of the forward momentum.
Generally, when going on a distance run, you roll from your heel to your toe. The majority of people run this way. If someone naturally runs on their toes, even when jogging, they usually do not look naturall. I have a friend like this. The whole run he leans forward and runs on his toes. He makes loud scuffing noises every time his toes hit the ground as well. I am begining to notice my little brother does this as well. It is as loud as a hippo.
Now if someone that doesn't naturally run this way tries to run on their heels, they look quite funny to, but in a different way. They are used to runing standing fairly straight up instead of leaning forward. So when they run on their toes, they stand sraight up and "prance" from toe to toe which forces them to bring thier knees up very high. This is not efficient or naturall looking.
I have been writing about distance running. When the pace increases however, form changes. The faster you are going, the more you need to shift to your toes. This is a natural tendency that just makes sense. For something like a 100 meter sprint, the athlete would be up on their toes the whole way. Some people however CAN'T run on their toes! These people are not sprinters and the best they can do is heel toe as fast as they can.
I don't believe that people should be trying to change their running forms in their parkour. There is no way that a traceur will be going at a 100 meter pace. When I run the 400 meter dash (1 lap), I don't even run the whole thing on my toes. At the begining and end for sure but in the middle, I roll slightly off my midfoot to my toes. A guy that went to my school last year ran 49.18 on the 400 meters. He was league champion and is now the fastest 400 er at Harvard. He has extremely long legs and heelstrikes the whole way around the track. He barely bends his knees. The point is, run how you naturally feel you should when doing parkour. Obviously you are still on your toes alot due to the fact you often need to explosively jump or hop skip in preparation for a vault. When you are just running though, heel toe is the smothest way. You gently roll with the momentum and then push off to continue it. When you run on your toes, every time you plant your foot, you are stopping the motion by planting down. This loses horizontal movement.
As for barefoot running: I understand the concept and all, but it doesn't work for anyone but those who naturally have perfect form. I'm talking side to side now. My feet are extremely pronated (they roll in). This give the appearance that I have flat feet when i am barefoot. But people with flat feet lack an arc in their bone structure. My bone structure does not lack arc but my tendons can not support the arc to stand up as it should. Instead, my foot rolls in. When i went to get my running shoes, my coach recognized this so he got me a shoe with a lot of support. I still got tendonitis in my achilies and in another tendon that is on the inside of the foot (can't remember the name). I had to go to physical therapy for months and then I went to a podiatrist. He explained everything to me and made me custom prescription orthodics (insoles). They have helped me alot (they better, they cost 500 bucks!!). As soon as I tried to race without them however, i nearly got a stress fracture. My podiatrist said that the support of shoes and orhtodics improve biomechanics and efficiency to the point that you can never run as efficiently barefoot as you could with them.
Also, pronation is in no way a rare condition. Many people have it and don't know until they start running or playing a sport involving running.
