Poor people don't think investment is a waste of time and they know that rich people increase their wealth by investing money. They don't want to invest their money because they think that if their investment turns negative they will lose their small money as well. Their lack of knowledge about money management let their fear dominate them.
You are correct from some examples of people around my city shows absolutely results of what you are saying. From op holding money in bank doesn't show any wiseness although it serves as a reserved fund to back up whatever expenses we are making but sometimes we also need to consider putting money in bank or saving money banks doesn't add any value to our income and to our life's rather we can access it at our pleased time. Instead of holding money bank it would ideal investing it is another means to secure more Income whereby the money invested has created another channels of income to our financial status.
Most time cutting down our expenses also positioned us to have some spare reserved funds with us, like what op highlighted and yet couldn't meet up paying our bills while we keep spending in an unnecessary things could either create more lost to us instead of adding. The only way to enjoy money is when it turns to assets by then we can spend some little percentage from the investment that is why today the rich always getting Richer while the poors keeps draining and swimming in adject poverty.