An interesting thing about taxes – ostensibly, they're used to destroy industries, but perversely they create an incentive for government to stimulate the very thing they're trying to destroy. For example, cigarette taxes are supposed to make smoking less attractive, ideally destroying the entire cigarette industry. But a government who wants revenue (as all governments do), will find that in order to maximize its revenue, it has to encourage smoking.
Applying this observation to progressive taxes in general leads to the following conclusion – taxing the rich, and sparing the poor leads to a government that perversely wants to encourage a wealth gap. When the government depends on revenue from the ultra-rich, they will naturally focus on making the ultra-rich even richer, particularly when that's easier than taking a poor person and making them ultra-rich.
By the same rationale, a government which has a broad based flat tax will be more inclined to improve the wealth of everyone, rather than simply the ultra-rich.