You can see that all the energy systems turn on together but the Alactic system (ATP-PC) provides the initial boost (because this energy is instantaneously available); then the glycolytic system takes over as the alactic system fatigues and diminishes in output; finally the aerobic system starts to predominate as oxygen becomes available (from your elevated heart rate).
The take-away is you should do your best to train all your energy systems to maintain adequate levels of ATP and keep your mitochondria healthy.
Just like you train for different types of muscle development (heavy load with low reps vs light weights and higher reps or running quarter mile sprints vs running 10K's), you should train the energy production systems too.
Get good at producing energy from various sources and for different demands. Your performance will increase and your mitochondria, the little power plants within each cell, will stay healthy too.
#1 - Lift Heavy Things
#2 - Increase Nutrient Density
#3 - Sprint Occasionally
#4 - If It's Good for You, Do It Every Day
#5 - Fast Intermittently Often
#6 - Keep Your Power Plants Running
The corollary to Rule #6 is the SAID principle (Specific Adaptation to Imposed Demands). It means you get good at what you do. So if you want to produce loads of energy efficiently and for all types of work, then you must force your energy system to work.
So do the right kind of training to stimulate the right kind of energy production so you become an effortless, efficient energy producing machine.
Rule #7 is next. There is some confusion on this one.