You've hit upon the most important and possibly most overlooked point in macroeconomics. At the level of the whole economy, modulo things like inventory, there's no way for aggregate savings to be anything other than aggregate consumption + investment. Every good or service is produced by someone and consumed by someone else. If you don't have both parties, there's no transaction.

When you "save" money, it's essentially a claim check against someone else's income. It's a way of recording that you contributed more than your fair share to the economy this time, so at some time in the future, you have the right to consume more than your fair share.

If everybody contributes more than their fair share, who's using up the excess? And then if they all go to cash in their claim checks at the same time - say, when the baby boomers retire - who'll produce the goods and services needed to satisfy those claim checks?

I haven't implemented this myself (yet), but perhaps the solution (for an individual) is to store value through scare resources (eg gold and other precious metals, maybe land) rather than through money (ie stored labour).

It still has the same problem: the price of gold goes up as everyone purchases claim checks denominated in it, and then crashes as everyone tries to cash out those claim checks for the goods and services they need to live.

The real solution is to store value in resources that increase the productive capacity tomorrow, so that when everyone tries to cash out their claim checks tomorrow, there will still be enough goods to satisfy them all. In other words, investment. The problem is that an investment is only a good investment when it increases the productive capacity for something that people actually want tomorrow. It does no good for everyone to invest in houses when they really need health care upon cashing out those claim checks.

And there are often technological barriers that prevent dollar investments from being productive. You can pump all the money into biotech research that you want, but you're still not going to get a cure for cancer until someone actually cures cancer. Innovation has a random element that isn't always amenable to throwing money at the problem.

People often wonder why the U.S. economy did so well after WW2, compared to the Depression before and the 1970s malaise afterwards. IMHO, it was because the large amount of pure scientific research undertaken during the war created a large stockpile of fundamental scientific breakthroughs that were ready to be exploited. All the hard, risky parts of innovation were already done, funded by the War Department, and so companies could readily transform surplus cash into innovations that made people's lives better in the future.