There is a welfare, or ethical, aspect to Smith’s political economy, which includes a bias towards the interests of the poor, and against wealth that arises from the less productive parts of the economy. However, these aspects of his thought do not lead him to state designed schemes for distributive justice. Rather he demands an end to those state activities which harm the poor, and the most productive parts of the economy. The assumption is that state action is to very limited, and beyond education, which Smith still believes should be largely private, he does not suggest expanded state activity on behalf of the poor, as distinct from the re-ordering of taxes and the regulation of the economy which itself tends towards deregulation. Herzog refers to negative externalities and asymmetries of power in the economy which are not addressed by Smith and which might have led him to expand the field of state action if he had lived long enough to see those issues become of more concern in political life and in political thought.
Answers to this kind of question are necessarily speculative, but we can get some idea by looking at where Smith can be located in relation to other thinkers of his time. Wilhelm von Humbolt who was writing a bit later in The Limits of State Action puts forward an eloquent case for minarchism, minimal state liberalism, which he refers to as proper polity or a state based on negative welfare. This includes a rejection of the kind of modest proposals Smith has for state activity with regard to public goods and the condition of the poor. There is not precise equivalent for Humboldt on the side of a very active state. Rousseau had a strong belief in the justice of income and wealth equality, but he thought it was only relevant circumstances where not much state action would be necessary to maintain that situation. There is some attention at some points to measures the state might take to restrain inequality, as in the proposed constitution for Corsica, though the concern is just as much with the moral corruption of leaving a locality and immediate community. The major arguments for an active and expanding state of Smith’s time come from the actions and brief texts of political actors, most famously the French minister Jean-Baptiste Colbert, and from a conservative position of maintaining an existing aristocratic-monarchical state.
The difficulty in comparing Smith with current thinkers is that ‘progressive’ thinkers of the 18th century favoured limited government, and now support expansive government. Those elements of 18th century thought which anticipate statist-active government progressive positions now are only accepted by Smith in their most moderate form and more than balanced by state limiting proposals. This suggests a libertarian-egalitarian liberal cross over, but more leaning to the libertarian side. The likelihood therefore is that Smith would have favoured very limited moderate steps on the issues raised by Herzog, and would have wished to cut back on big schemes to restructure the distributive effects of the market.
Smith’s view of distributive justice early on in Lectures on Jurisprudence, where he invokes Aristotle and Grotius to discuss the distinction between commutative justice and distributive justice. Commutative justice refers to what cannot be taken from us or attacked, because it rightly belongs to us, or is part of us. It is a very strong form of justice relative to distributive justice. Commutative justice is enforced through the state legal system, distributive justice is a matter or morally preferably outcomes in which we prefer to see wealth going to those in need rather than those who already have many luxuries. Smith never directly says that all distributive justice should become a voluntary matter never enforced by the state, though that might seem to follow. He also refers, as we have seen, to the relation between politics and issues of ideals of distribution, the inevitability of the ways that the state tries to maintain itself though distributive strategies. Smith may think that distributive justice is in a middle position between the institutions of criminal justice which enforce commutative justice (strictly speaking) and the purely individual voluntary nature of charitable giving. Distributive justice is something pursued by the state for the sake of social peace, and the maintaining of itself, as a precondition for social existence, but not a matter of absolute justice.