ATP synthase is a protein assembly in the inner mitochondrial membrane. Proton pumping ATP synthase is a multisubunit transmembrane protein. The proton pumps expel H+ from inside to outside of the inner membrane.
So there is high H+ concentration outside the inner membrane. This causes H+ to enter into the mitochondria. This proton influx causes ATP synthesis by ATP synthase.
In biological systems, the chemical reactions concerning glucose and ATP as a product are vital for cellular respiration and photosynthesis. Shortcuts reduce the activation energy, which increases the net "gain" of products. I would go with the last one.
