To address this question, consider two different aspects of redistribution: anti-poverty programs that benefit the poor, and general redistribution that transfers income from richer to poorer at every point on the distribution. Welfare, Food Stamps, and Medicaid are examples of anti-poverty programs. Progressive income taxation is the standard example of general redistribution.
Proponents of anti-poverty programs rely mainly on one or more of the following arguments:
that society should care for the poor out of compassion;
that everyone benefits from alleviating poverty, but since some people might free ride on the charitable actions of others, government must force everyone to contribute;
that private markets do not supply sufficient “income insurance,” so government must intervene;
that a dollar means more to someone in poverty than to Bill Gates, so government can increase aggregate utility by transferring from rich to poor;
that anti-poverty programs prevent revolution;
that anti-poverty programs make it easier for society to avoid distorting policies like rent control or minimum wages.
None of the arguments for anti-poverty programs, however, applies with the same degree of force to general redistribution. Setting aside the low end of the distribution, high incomes result partly from luck but also from greater effort, longer hours, willingness to accept risk or unpleasant working conditions, and so on. Moreover, general attempts to redistribute income discourage work and saving far more than (well-designed) anti-poverty programs.
These concerns do not “prove” general redistribution is a horrible policy. And some degree of general redistribution is likely even in the simplest possible tax system. But the main focus of redistribution should be anti-poverty programs, not broader redistribution or “soak the rich” objectives.