> Savings being equal to investment isn't a material fact, it's an assumption built into some macroeconomic models. In order for savings to turn into an asset that increases production capacity (which is what we hope it's for), someone has to spend the money on building a new asset (or improving an existing one).
Correct. I think the definition of savings in economics is wrong. I would suggest that the distinction between savings and investment is in with how much difficulty you can reverse your decision (that is, liquidity of the underlying asset). The boundary is fuzzy, but it is important to consider.
So for instance, if I buy a new production line for cars, I cannot easily sell it (for the same price). I am hoping that it was a good decision, because it's hard to reverse (if I see tomorrow, that people actually don't want cars, I cannot easily start to make tractors). That is a decision which is investment.
On the other hand, if I buy shares in a car company, and tomorrow I see that people don't want cars, I can change my mind, sell the shares, and buy some other company. This is savings, not investment.
The reason why the reversibility is important is because if you are an economic actor and make an irreversible decision (like purchasing/building a production line), then other actors in the economy, who have savings, gain a certain advantage - they can react to your decision. They can follow, or they can avoid your investment, depending on how it pans out.
This follows it's not always wise to invest, to make an irreversible decision. Sometimes it's better to wait - and that is saving. Therefore the distinction between savings and investment is actually very important for even macroeconomics. If you have an economy where everybody is waiting for good opportunity (saving), then there is no economic growth. They still can "formally" be investing (buying shares or other financial instruments from each other), but the irreversible (i.e. real) decisions do not get made.