What determines a load's current requirements?
Using the water analogy, a 10 mm pipe will only allow a certain amount of water to pass, and it will depend on the applied pressure. If you double the pressure, the flow will double.

A certain material will require a certain voltage to flow a certain current. Quoting a nice answer in Physics.SE about gravitation:


  Physics [Ohm's law] does not answer existential problems. It gathers data and observations and models them with mathematical equations and functions, and then can explain the data with the model and predict new observations.