As someone who learned the "right" way in German public school about 20 years ago, the statement "teaching people what was actually happening with subtraction" is completely indecipherable to me. Maybe I never learned what subtraction is. To me it's like advocating for not using a ruler because that would somehow forego teaching people what measuring actually means.
Both "measure" and "subtract" can mean doing any number of things in mathematics, depending on what you're dealing with. Intuition for things in the physical world specifically shouldn't be a goal of teaching mathematics at school. It's a prerequisite. If a child already can't grasp the concept of taking away from something, throwing mathematics and numbers at them is not going to help one bit.
Both "measure" and "subtract" can mean doing any number of things in mathematics, depending on what you're dealing with. Intuition for things in the physical world specifically shouldn't be a goal of teaching mathematics at school. It's a prerequisite. If a child already can't grasp the concept of taking away from something, throwing mathematics and numbers at them is not going to help one bit.