While the study in the OP is poorly done..

> Who cares about socialist propaganda like this?

Discussing inequality in society isn't "socialist propaganda".

> There is no evidence that "equality" in the distribution of wealth is good for middle class and low income persons.

https://www.americanprogress.org/wp-content/uploads/2013/12/...

> The evidence suggests that the channel through which inequality hurts growth
is asset bubbles and financial-market instability, so policies that impose adequate oversight in that sector also flow from this research

http://www.oecd.org/social/Focus-Inequality-and-Growth-2014....

> The evidence is strongly in favour of one particular theory for how inequality affects growth: by hindering human capital accumulation income inequality undermines
education opportunities for disadvantaged individuals, lowering social mobility and hampering skills development.

There is evidence that the current level of inequality contributes to toxic asset bubbles and the quality of human labor available to industry. I'm not sure how improving both those situations are "bad" for the average person?

> For example, if the distribution were more equal on a relative basis, but all brackets had less money than before, is that supposed to be an improvement?

Yeah, that isn't how it works. Hint: The biggest gains are via education subsidization & shifting the tax burden.

Hell, it can be done with just shifting money from Defense -> Education and removing clauses in the tax code that primarily benefit those making 6 figures. [i.e. Capital gains tricks for multiple residences, mortgage interest exemptions]

No one says "get rid of inequality at any cost" but rather "How can we improve growth by reducing inequality?"

http://www.oecd.org/eco/growth/49421421.pdf

> Reforms to increase human capital are important for improving living standards, and
are also likely to reduce labour income inequality. New analysis shows that a rise in the
share of workers with upper secondary education is associated with a decline in labour
earnings inequality (Fournier and Koske, 2012). Examples of policy initiatives to raise
upper secondary education attainment include inter alia enhanced accountability for
schools, better teacher recruitment and training, and special support for pupils at risk of
dropping out.

> Raising social mobility by making educational outcomes less dependent on personal
and social circumstances should boost GDP per capita by enhancing entrepreneurship, the
overall quality and allocation of human capital and, ultimately, productivity.

> Taxes do not only affect the distribution of income; they also affect GDP per capita by
influencing labour use and productivity, or both (Johansson et al., 2008). Some tax reforms
appear to be win-win options – improving growth prospects while narrowing the
distribution of income. Many, however, may imply trade-offs between these objectives.
Following the same approach as for labour market, product market and education policies
discussed above (Table 5.2), these complementarities and trade-offs are drawn out in

> Reduce distortions in taxing capital income. Tax relief – such as reduced taxation for capital
gains from the sale of a principal or secondary residence – often distorts resource
allocation without boosting aggregate savings and growth, and benefits mainly
high-income groups. Specific tax relief may also provide tax avoidance instruments for
top-income earners. In particular, there is little justification for tax breaks for stock
options and carried interest. Raising such taxes would increase equity and allow a
growth-enhancing cut in marginal labour income tax rates.

> Re-assess tax expenditures that benefit mainly high-income groups (e.g. tax relief on mortgage
interest). Cutting back such tax expenditures is likely to be beneficial both for long-term
GDP per capita, allowing a reduction in marginal tax rates, and for a more equitable
distribution of income. Lowering tax expenditures would also reduce the complexity of
the tax system, and thus tax compliance and collection costs.