Regardless of the morality of progressive taxes, the economical benefit of progressive tax is at least debatable. But could a highly progressive tax replace at least some of the american/european anti-trust regulations?
Progressive income taxes on individuals is not very likely to have any real impact on market power, but progressive income taxes on corporations can certainly have this effect. The key idea is that in many industries (for example, the financial industry), there are geniune economies of scale: having a big balance sheet allows an investment bank to take advantage of various synergies, meet demand from customers at lower costs and therefore at lower prices. This means that there is a natural pressure towards concentration in the financial industry. High levels of concentration, however, allow firms to price out their competitors from the market due to their size and the aforementioned scale effects, and can lead to a scenario of oligopoly.
The government can try to deal with this problem by introducing negative incentives for corporations to get bigger. This can be in the form of an explicit limit on the size of corporate balance sheets rel to GDP, as advocated by Stiglitz, or it can be in the form of income taxes, or capital requirements, which are "progressive" in the sense that they impose higher marginal costs on larger and more complex firms over smaller ones. Such a measure can offset the natural incentive towards aggregation in the financial industry, for example. This is already done to some extent by Dodd-Frank (perhaps unintentionally) in the US, which raised capital requirements for SIFIs (which are well-integrated financial institutions with large balance sheets). The adverse effect is that by doing this, a country can effectively price its financial institutions out of international markets.
In turn, a policy which reduces market power can have positive effects on the income distribution, as it would lead to lower prices and higher wages. The problem is to find the right balance between the benefits (lower costs) and costs (market power) of concentration in the marketplace.