Why Does Nature Favor the Principle of Least Action?

[dEdt]

Hamilton's principle says that the action for the true path that a system follows will be stationary. As I understand it, the action is almost always least. Is there a reason why nature prefers least action rather over greatest action?

 

[Marioeden]

Hamilton's principle says that the action will be stationary but we can certainly say that it won't be a maximum because we can always increase S by taking a faster, wiggly path with T>>0 so you know it won't be a maximum.

However it could still be a saddle point but "Principle of stationary action" doesn't sound as cool as "Principle of Least Action"