I am 100 percent in favor of training privates to assume leadership roles,but basic training is not the place for this. It should be done at their permanent duty assignment,where they are surrounded by others from E-1 to E-7 that are already doing the job that can monitor and help them learn the leadership roles in combat,and more importantly,WHY the leadership requires them to do the things they must do.
In MY opinion this is easier to learn and better understood at the unit level,where you will be serving with the same people for 3 years or more,NOT with other trainees or cadre you may never see again.
Plus,in real life various army divisions have specific areas of interest they train for that is the focus of their training. You train different to go into South America than you do the Swiss Alps,for instance. Just like you train different to go to war in a jungle than you do a desert.
For the military,terrain and climate are everything.