> it means that the balance between potential (simplified stored ) and kinetic (simplified spent) energy should on average be kept as close as possible despite constraints.

Is that what it is saying though? It is the difference that is being minimized, not the absolute difference. Seems to favor big gaps in favour of PE.

Principle of least action is really the principle of stationary which does not have any preference for the actual size of the gap.

Even if it is true how would one justify it as an axiom, as opposed to deriving it from other principles?