I don't think that's a valid statement. There is only so much 'stuff' that you can use. Beyond a certain level more money does not translate into a better quality of life or more 'stuff' for most people, there are a few outliers but lots of very wealthy people are actually quite modest. They're so modest you won't read about them in the newspapers.
Although demand in the economic sense sort-of-sounds like want - certainly I'd like a new Lamborghini - I have zero effect on the demand for lamborghinis.
The level of spending (poverty vs wealth) is mostly irrelevant because that's a value line someone draws on a graph somewhere. Poverty in the Midwest is not the same as poverty in Sub-Saharan Africa. Absolute Poverty (in which a person has insufficient resources to survive) has a wide variety of causes but essentially reduces down to the inability of an individual or family to produce enough to exchange for what they need.
Savings are just postponed consumption in the same way as debt is the promise to hand over your future production.
Savings are just postponed consumption, but if the consumptions of multiple people never align (you could save until you're dead) the aggregate demand will never rise to a high level.
Keynes had to kill the idea that production is the foundation of growth in an economy. He did this by implanting the idea that production is irrelevant, all you needed as spending (the fantasy of aggregate demand). This was further pushed by the universal declaration that savings were a problem because it was postponed - rather than transferred. Once this foundation was laid, the idea that throwing more money at people would increase wealth was created, and enthusiastically adopted by politicians who could use it as an excuse to throw money around in good times and bad.
Savings are the foundation of future production, and future production is the foundation of future wealth. This is so self evident it takes a high level of internal contradictions to believe it not to be so.
What you are saying sounds so easy, but if it were, there wouldn't be recessions or liquidity traps. You're right that production is key, but if the monetary system becomes friction in between producers and consumers, then problems can arise even if production is okay. I don't really see a contradiction here. Savings are the foundation of future wealth, but if nobody spends any money, businesses crumble, and capacity is lost. When people decide to spend again, it takes time for the economy to recover.
The issue is you'd have to - and get everyone else to - understand that periods of high interest rates and periods of low wages would periodically happen. But people expect wages to never fall and are conditioned to fixed interest rates. As lowering wages is unacceptable the solution is to cut positions, which arguably makes things worse as no job is worse than a lower payment on an existing job. So we are doomed to business cycles for the foreseeable future.
The key thing I believe most people miss is that they believe that 'economic stimulus' in terms of under priced interest rates, government borrowing and foolish spending and other tricks comes at no cost. But there is a very real cost, and that is misallocated production - building value-destroying 'bridges to nowhere' and burdening of future income with excess taxation to repay debt.
There are those who say that a sclerotic economy - such as most countries have had for going on 7 years now - is better than a short, sharp contraction. You can compare the experiences of Japan - flat growth for two decades - or countries like Estonia and Latvia which had massive contractions but bounced back to strong growth relatively quickly. How much that impacts the safety and stability of society may be related to social cohesion and personal savings.
Probably the best answer is that governments keep a rainy-day-fund, and when credit contracts due to external shocks, the government gives a temporary tax receipts holiday and spends the savings. Such a strategy would allow people to have confidence going into an economic contraction but wouldn't indebt the government to the future. But it is fantasy-land to expect any politician to design such a scheme and resist the temptation to raid it for votes.