You clearly have never played football. If you lead with your head, you're going to get your block knocked off. Your head can't push with the same force as a shoulder can, nor would you want it to. It houses some rather precious squishy stuff, so try to have it force aside something much harder/difficult to move is a bad idea.

In general, a running back is taught to lead with their shoulder. As a defensive back, you normally attempt to lead into a tackle with your shoulder, then wrap up the ball carrier and take them to the ground. As you can clearly see, that is a)not what will happen evertime and b)sometimes people are bad with their basic mechanical skills.

As for the hardness of the helmets: the helmet has to be rigid or it won't be able to properly protect a persons' head. The inside then has an about 1" thick layer of padding that lessons the force of any impact with it. Thanks to the fact that everyone is wearing pads/helmets, the feeling of impacts are lessened significantly. It can still hurt like a mofo, and often does given the fact that people fly around as hard and fast as they can go, but whenever a helmet collides with a padded area/other helmet, it doesn't work quite the way I think you imagine it does.

Source: played football for over a decade in elementary school, high school, and college. Given (and received) hits like the one in gif.