The people that tell you to keep your knees behind your toes as you squat are often the same double-thinking people telling you to use your legs when picking something heavy off the floor. Sorry to burst your bubble, but to use the legs, and by contrast not your back, when lifting something heavy off the floor the knees have to travel past the toes. Those are two pieces of advice contradict one another.
Where did this even come from? Myths are like the a game of "Telephone" or "Chinese whispers". They start off as a study of some sorts that was misinterpreted and passed on from one person to the other, until a couple of decades later when that misinterpreted knowledge is deemed as indisputable. And now, every decent person who can see the absurdity with this, so-called, indisputable fact has to talk some sense into people who actually believe that their knees will either explode or develop acute osteoarthritis from the second their knees go past their toes.
Fry, Smith & Schilling, did a study in 2003, "effect of knee position on hip and knee torques during the barbell squat" (PDF available below), where they showed with the most basic test on how the squat can change based on knee travel. They compared a restricted squat, where the knees were unable to pass the knees, and an unrestricted squat. To our surprise, the results did not show any exploding knees, nor did the participants show any signs of acute osteoarthritis. What they did show, however, was positional changes at the ankles, knees, hips, and most importantly, in my opinion, anyway, was the change of torso inclination. By allowing the knees to track past the toes the trunk will be more vertical. Or in other words, to have a more upright posture when squatting, you have to allow the knees to track freely forwards, even it that means past the toes.
This is interesting for two reasons. Firstly, by staying more upright during the back squat the demand of the quadricep muscles increases — Just what a weightlifter needs from a back squat — Secondly, by staying more upright the shear forces acting on the lumbar spine decrease. It's for this exact reason bracing is so important during a squat. It is to reduce shearing forces, since higher shearing forces are closer correlated to lumbar spine injuries, compared to tension or compression forces. So, by allowing your knees to track freely past your toes and as a result allowing you to stay more upright you, along with utilising the quadriceps more, simultaneously decrease the risk of injuring the lumbar spine through excessive shear forces. #winwin
The sum of the forces acting on the body as a whole when squatting, let's say, 100kg will always be the same. However, you can distribute those forces between the joints in your body. By allowing the knees the travel forward you shift those forces away from the lumbar spine. But as mentioned above, the total sum is still the same, even if it has moved away from the lumbar spine. The forces have just moved to a different location/joint. With the allowance of unrestricted knee travel the forces acting on the knees will increase, there is no way around it. Now, this does not mean that your knees can't handle the extra load, I can assure you that they can. I'm telling you this to illustrate the fact that the decision for allowing the knees to travel forwards you distribute the forces more evenly through the body. Where the majority of the forces beforehand were in the lumbar spine are now more evenly distributed between the lumbar spine and the knees (and other joints of course).
When you wear weightlifting shoe it is essentially providing you with additional dorsiflexion at your ankle. This allows for the knees to travel even further past the toes than they could previously, without the shoes. The effects are similar to those previously mentioned, just in a bit more excessive, if you will. As weightlifters,