I'm afraid you did not understand the meaning of Noether's theorem, nor the sense of what is written in my article... And in general it would be better for you first to speak with Gottfried Leibniz, and not with Noether
The law of conservation of energy in mechanics in its present form is the greatest mistake of physics during its entire existence. This error arose because of incorrect assumptions made more than 300 years ago by the Cartesians and Gottfried Leibniz. Correction of past mistakes is always the most urgent issue for any science, especially in the theoretical and methodological terms. See more: https://www.academia.edu/36208608/The_current_law_of_conservation_of_energy_is_greatest_mistake