As far as I can tell, the best alternative to (nearly) strict equality of income is marginal productivity theory: each person should receive the social permission to consume socially produced goods and services in proportion to his or her marginal productivity. People who are very productive at the margin receive more of the social product; people who are not very productive should receive less.
Of course, arguing against one alternative among many is not much of an argument for a position, but knocking down the best alternative offers better support.
It's notable that Mankiw makes a deontic moral argument for marginalism rather than a utilitarian or pragmatic argument. I suppose he must, because the utilitarian argument looks pretty bad.
What do we mean by the marginal product? Generally speaking, the marginal product of something is the productivity of adding one more of that something; if we model production as a continuous function, the marginal product is the slope (partial derivative) of that something's contribution to production.
One problem, then, is that for an individual competitive firm, wages are exogenous: nothing the firm can do can affect wages. Thus the firm hires labor until the wage of the last worker exactly equals his or her contribution to production. At the level of the individual firm, therefore, the causality is exactly the reverse of the marginalist story: people are not paid according to their marginal productivity; the firm employs people until their marginal productivity equals their pay. If the prevailing wage were to exogenously increase or decrease, the marginal product of labor would still, at each individual firm, be equal to the wage.
But if the wage is exogenous to the individual firm, how is it set? Well, capitalism is very careful (with a notable exception, finally corrected, in the last half of the twentieth century) to ensure that most people's wages are set in a perfectly competitive market. In a perfectly competitive market, prices fall to costs, i.e. the cost of labor power, i.e. the cost of minimal subsistence. Only political reasons, not economic reasons, push some wages above subsistence in the long run. (In the short run, demand for a new specialty, such as computer programming, can race ahead of supply, allowing specialists oligopoly pricing, but after ten or twenty years, supply will eventually catch up.)
Thus, marginalism entails that most people should receive subsistence wages; not because most people can produce only that much, but because we will hire labor until the last person hired produces that much. And they produce that much not because of their personal characteristics, but because the firm has made a choice between labor and capital based on the exogenous subsistence wage. I can't imagine that anyone would consider these circumstances "fair."
What about the capitalist? Even allowing the polite fiction that capital (machines, trucks, buildings) produce anything at all, the capitalist himself produces nothing; he just sits around owning things. Even if the marginal product of capital is equal to the wage, an individual capitalist, unlike a worker, can own an unlimited amount of capital. Moreover, the more capital a capitalist owns, the more he can acquire, so capital ownership, absent political limits, is self-concentrating. And, concentrated enough, the capitalist can enjoy monopoly pricing, exogenously setting the price of capital. And again, firms will choose just enough capital so that the marginal product of capital is equal to its price.
So, yes, everyone receives his or her marginal product, but the decision about what that marginal product should be is not economically but socially determined; it has nothing to do with any individual's characteristics or capabilities. Fair? I think not.
What about the millionaire CEO? Is he paid his marginal product? If so, if the marginal product of a CEO really is in the eight figures, then bog-standard economic theory tells us we should be producing a lot more CEOs. We should be producing so many CEOs that the last one we hire produces the subsistence wage. If the CEOs we have are really producing tens of millions of dollars per year, we should experience an enormous boost in productivity by vastly expanding the number of CEOs.
Heh. Not gonna happen. Even if it's true that each CEO really is directly responsible for tens of millions of dollars of productivity (they're not), the fact that we have politically limited the supply of CEOs is why their marginal productivity is so high. And, of course, a CEO's marginal productivity is not really that high; they are pseudo-capitalists, paid not for their productivity but their social status.
Fundamentally, the problem with marginal productivity theory is that marginal productivity is politically determined; marginal productivity precedes wages and prices of capital.
There are, of course, limits on these prices. There is a physical limit as to how far real wages can fall, there are political pressures keeping wages above mud huts and just enough food to avoid starvation, and given some politically determined wage, there are high and low limits on the marginal productivity of capital. However, within those limits, marginalism entails that most people should live as poorly as possible, and that a small few should live as wealthily as possible, regardless of the individuals' characteristics, and regardless of the potential productive forces of society. Marginalism moves us away from the shared goal of abundance.
Another way of looking at it is that yes, it is a matter of economic necessity that everyone does in fact receive his or her marginal productivity; however, within physical limits, we are free to set marginal productivity. And if we are free to set it, we are free to set it such that everyone's marginal productivity is nearly equal. As productivity increases, equality tends to increase, until we really do have abundance and absolute income equality, i.e. as much as everyone wants.