This is an overly simplistic analysis. Empirically, if you give a poor person $1, they will spend more and save less than if you gave a wealthy person $1, with the effect more pronounced the wealthier that person is. In other words, the poor have a higher marginal propensity to consume. As for why spending > saving, at least for GDP, the economy is driven more by demand and consumption, than by investment. Startups would be nothing in the absence of demand. Startups would still exist in the absence of investment. If you break down GDP into its constituent parts, the number 1 contributor (>50%) is consumption.
I also think it provides an interesting perspective to view the government from a political and demographic angle. The government is (theoretically) the will of the majority (or supermajority, in some circumstances), with some protection for minority interests. Consider then that the median US income is $52,762 per year. Consider then that 51% of the population is going to make between $0-54k. Since it is in their economic interest to "offload" their tax burden, it is inevitable that the tax system would be progressive. The tendency towards a progressive tax system is tempered only by the fact that most people do own some wealth, the low/middle-classes own desire to be wealthy, and the economic necessity of rewarding people to grow the economy. This does not always apply since people are not always rational. I'm only saying that this is the reality.