That's a fine idea, but few people will do that in practice because they don't want any risk at all in losing the money they're saving for those things. People generally invest for the very long-term, like retirement, not for things like house downpayments.
Consider the humble savings account. Those accounts may be dollar-denominated, but under the hood they're really a type of security. You're making a loan to the bank at interest - a special kind of loan that you can call at any time, in part or in full, but a loan all the same. The bank then takes that money and loans it out at interest to people who want to borrow money to buy houses cars, whatever.
There is risk involved - the people at the end of the chain might default on their loans, in which case the bank loses their money. Historically, if the bank lost enough money then they wouldn't be able to pay back the money they borrowed from you, in which case you also lose it. Nowadays banks are required to carry deposit insurance, so instead when the bank defaults the FDIC loses their money, but you still get paid. But if enough banks default then the FDIC also won't be able to make good on their guarantee to you, and you're still out your money. Meaning that when you stick your cash in a savings account, it's not really money anymore. It's an IOU - a promise to give you money when you ask for it. Probably.
> few people will do that in practice because they don't want any risk at all in losing the money they're saving for those things.
Many people do it in practice. Stuffing dollars in your mattress is "saving dollars". Loaning money at interest who will aggregate it with other money and invest in productive assets is an indirect investment in productive assets other than dollars.