A nice little response from Daron Acemoglu which reinforce what we have previously discussed. Yes, it matters because economic and political power are interlinked :
Here are three main reasons why society may care about inequality. First, people's well-being may directly depend on inequality, for example, because they view a highly unequal society as unfair or because the utility loss due to low status of the have-nots may be greater than the utility gain due to the higher status of the haves. Second and more importantly, equality of opportunity may be harder to achieve in an unequal society. Many economists have, by and large rightly, focused more on poverty than inequality. Poverty not only causes low standards of living and poor health but damages both individuals and society by preventing those at the bottom from realising their potential, perhaps because they are unable to obtain a decent quality of education to prepare them for competition in the labour market. While poverty is clearly the more important factor in creating a non-level playing field, inequality may also be a nontrivial factor: those with greater wealth provide to their children resources and thus opportunities that the less wealthy cannot, and this may make it more difficult for society to achieve equality of opportunity.
Third and most importantly, inequality impacts politics. Economic power tends to beget political power even in democratic and pluralistic societies. In the United States, this tends to work through campaign contributions and access to politicians that wealth and money tend to buy. This political channel implies another, potentially more powerful and distortionary link between inequality and a non-level playing field. It may also create pathways from inequality to instability, because both the economic and political implications of inequality can create various backlashes.
The structure of inequality is not only a deeply political issue because of inequality's impact on politics but also because the extent of inequality is shaped in part by politics. The recent changes in wage and income inequality in the United States illustrate this. The substantial increase in inequality in the US labour market since the late 1970s undoubtedly has many economic causes, including the slowdown in the supply of skills and the increase in the demand for skills driven by new technologies and globalisation (see this, for example), though some economists also see political factors at work here, like those associated with the weakening of unions. But the purely economic factors are unlikely to account for the massive increase in top inequality—inequality between the top 1% or even the top 0.1% and the rest of society. As research by Thomas Piketty and Emmanuel Saez documents there has been a perhaps unprecedented increase in how much of total national income is captured by the very rich and the very wealthy.
A case can be made that top inequality has been soaring in part because of politics. Piketty and Saez document that the very rich today are different than those several decades ago, most importantly because they are not rentiers enjoying returns on their or their parents' capital, but W-2 earners, enjoying very, very high salaries. Recent research by Thomas Philippon and Ariel Resheff shows a concurrent increase in salaries in the financial sector relative to the rest of the economy, confirming the pattern suggested by casual empiricism that many of these very high W-2 earners are in the financial sector. But the expansion of the financial sector and the salaries therein over the last two decades may not have been just an unavoidable consequence of economic tides but a very political process. The deregulation of finance, despite the presence of implicit and explicit government guarantees to financial institutions which would have ordinarily necessitated significant regulation, appears to have been partly won by the financial industry as a result of lobbying, campaign contributions and the access to politicians that the industry enjoys (though this is not to argue that some of this deregulation did not have a compelling economic logic nor that free-market ideology played no role).
If so, politics may have been the key factor in setting in motion the forces that have led to the massive rise in top inequality and also shaped the path of development of the financial industry which arguably played a central role in the making of the recent financial crisis. This underscores a particular connection between inequality and economic instability over last three decades, though both of these are in turn caused by underlying political forces. Going forward, however, politics may play out differently, creating yet even closer connections between inequality and instability. As the lie of the land as far as finance, political connections and inequality are concerned haven't changed, we may witness further increases in inequality underpinned by continuing close connections between the financial industry and politicians. And this may lead to a strong backlash, taking aim not only at the super-rich in the financial sector but also at those in other sectors. While inequality in general may create various economic, social and political problems for society, sweeping actions against the rich would likely do more harm than good as it would hurt the vital entrepreneurial dynamics of the US economy in innovative sectors such as software, telecommunications or biotech.