S=I is tautological, from the definition of the model.
One guy had $1000 and no solar panels, another guy has $0 and 1 solar panel, maybe they trade.
What changes about your definition of savings and investment if they do or don't trade?
Nothing.
> People make the mistake of thinking savings are desirable
as compared to what?
> not understanding that formal language has separated the idea of savings
I assure you every economist knows the difference between putting money in a bank and manufacturing a car.
S=I says nothing about the usefulness, causality, or predictions about the economy. It would be like determining the state of a business by whether their assets equal liabilities.
If assets != liabilities, you have an accounting error, not an unprofitable business.