I think a more simple way to think about it is this:
When you purchase a piece of equipment, you pay out the full value of it immediately in cash, which is shown as an investing activity on the cash flow statement. If you counted depreciation expense as a cash output as well, by the end of the asset’s useful life you would be saying your cash decreased 2x what you actually paid.
Essentially the cash output is already shown in full in investing activities, so you don’t show it again in operating activities.
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