Taken as a whole, I would suggest that in "A Modest Proposal," Jonathan Swift's satire works on two distinct levels. First, Swift is addressing the problem of poverty within Ireland (a problem that is closely intertwined with the history of exploitation which England and Scotland were, themselves, culpable in creating). Secondly, he is levying a criticism against Enlightenment-era rationalism (a criticism reflected within the pamphlet's reasoned tone and style of argumentation, even as it advocates for the cannibalization of children).
Ultimately, Swift seems to be arguing that the problems facing Ireland are severe and require real solutions: solutions that must be based in an empathetic and humanistic perspective which pure rationalism would fail to provide.
Taken purely as a work of literature, "A Modest Proposal" must be viewed as highly successful. It still maintains its reputation as a satirical masterpiece into the present day. However, taken as a work intended to create real political change, its success is far less convincing. It did not achieve the kind of humane solutions which Swift was calling for concerning Ireland, nor did it do much to blunt Enlightenment era rationalism's preeminence within intellectual circles.
Regardless, Swift's reputation as one of literature's most accomplished satirists is well secure, through works such as "A Modest Proposal" and, perhaps most of all, Gulliver's Travels.
Swift wrote this satiric essay in frustration after a series of reasonable ideas he proposed to help the poor were ignored. These ideas are outlined briefly in "A Modest Proposal" and include such things as a modest tax on wealthy absentee landlords. But his main target is the type of person exemplified by his narrator: a person who can't see "the poor" as more than an economic problem to be solved, that treats them as economic widgets, and that denies them their humanity. Behind this lies a more general condemnation of people's hard-heartedness in letting truly horrific poverty exist in Ireland when it could have been relatively easily alleviated. The essay also attacks the hypocrisy that would allow the rich to rationalize "devouring" the poor in "ordinary" ways, such as by charging exorbitant rents, but would react in horror to actually devouring the babies of the poor. Swift, in essence, is saying: you are already, indirectly, "eating" the children of the poor. If that horrifies you, maybe you should try to solve the problem of acute poverty.
While the essay is "successful" in the sense of becoming a classic example of satire in the English language, it failed to change conditions for the poor in Ireland. Rather than look in the mirror and change their own behavior, the people Swift targeted labeled Swift a "misanthrope." They essentially blamed the messenger for delivering the message rather than asking why such a message needed to be delivered.
Swift has several targets in "A Modest Proposal." One is Great Britain. It was British rule that played a major role in creating the horrible conditions in Ireland referenced by Swift in the essay. Ireland was a colonial possession of Britain in the early eighteenth century, and much of its land was owned by absentee British landowners who gleaned much of their wealth from Ireland even as the Irish people lived in wretched poverty. So Swift, born in Ireland to relatively wealthy English parents, is attacking this serious social problem in the essay. He is also satirizing the emerging "Enlightened" philosophers who looked to statistics and rationalism for answers to society's problems. These people, like Swift's narrator, viewed human beings as numbers only, and Swift is pointing out that any solution to a social problem that does not put humanity first is immoral. One might also argue that he was satirizing the haughty approach to the poor that had developed in British society, one which assumed that poverty was the result of some sort of moral deficiency or laziness on the part of the poor.