Spending is crucial because that's what signals where investment is needed / desirable. Furthermore, spending is what gives companies profits that can then be reinvested for sustained development. If there is no spending, then investment is simply pointless.

If investment happens in a vacuum, without regard for where the demand (which is nearly a synonym for spending) is, the investment will likely go to inefficient or useless projects.

Furthermore, the stated causality from saving to investment doesn't exist in our modern financial system. Banks create money out of nothing whenever they find a suitable borrower. Of course, a borrower is more likely to be suitable if they can demonstrate demand for their product - again, the importance of spending.

Sidenote: There is an equality of savings and investment in the national accounts (if you ignore the external sector), but that's just an after-the-fact accounting identity without any causal content. There's good reason to believe that, if anything, the causality goes from investment to savings. Either way, it's not an interesting causality. The real economic decisions, certainly the ones that lead to good allocation of capital, follow where the demand is.

Sidenote #2: Your stab at the government misses the point as well. Nobody is asking for the government to start investing in productive capacity for things that the private sector usually provides.

However, government could ensure that people have more disposable income. This leads to more spending, which encourages (and finances, via reinvested profits!) investment in order to satisfy the added demand. At the same time, it improves the quality of the demand signal, which helps achieve a better overall allocation of capital.

There are other useful things that governments could do, but this is an important and useful thing. The economy generally works well when people can just vote with their wallets. But one precondition is that there is money in those wallets.