Hume’s Enquiries are not properly read as a collection of essays, in the way, say, his essays are. He changed the title, we should take him seriously (and his final chosen title for the entire shmeer was Essays and Treatises on several subjects).
I think it's a little more complicated than this. I agree entirely that we should take Hume's re-titling seriously. But I think we should also take seriously the fact that this re-titling occurs late in the game -- very late in the game for the Enquiry Concerning Human Understanding.
The first edition of the ECHU was published under the title, Philosophical Essays concerning Human Understanding. Likewise, Hume initially referred to the Enquiry Concerning Principles of Morals as essays (although under that title); this is how he refers to them in letters, and in the actual first edition that is what they are called within the body of the text itself -- it is only in the errata that he starts changing this. That is to say, if we take 'Enquiry' to indicate that the works should not be read as collections of essays, in both cases this comes out late: they were both mostly written, and the ECHU wholly written, published, and reprinted, as essays. It is only after the ECPM that he changes the title to Enquiry. Likewise, it's true that he eventually calls the whole group Essays and Treatises on Several Subjects, and obviously the Essays, Moral, Political, and Literary, are essays, but it's not clear that ECHU and ECPM fit into the 'Treatise' part, or even that 'Essays' and 'Treatises' are mutually exclusive categories.
Thus ECHU owes nothing of its structure to any conception of it as anything other than a special set of essays. Now, obviously these essays are obviously interrelated, and there is obviously at least some progression among them. They all contribute to one theme. And there's no question that these essays are all contributions to one philosophical investigation. 'Enquiry' is quite a good name for the set. But as Beauchamp points out somewhere, there's no reason to think that in changing the title from 'Philosophical Essays' to 'Enquiry' and calling the various parts of it 'Sections' rather than 'Essays' that he's saying that the Sections don't fall into the genre of essays; 'Enquiry' is a function-term not a genre-term. It doesn't identify the literary character of the pieces, but merely establishes what philosophical task they are being used to perform.
So, practically speaking, what effect does this have on interpretation of ECHU? I think our practice should be to read it as both a collection of essays and as an integrated investigation, because it manifestly is both. We should take seriously that Hume eventually re-titled it as 'An Enquiry', but we also have to take seriously that he wrote them as essays, and published them as essays, and only later re-titled them. (The argument for ECPM is a bit more complicated, since the presentation of it as a single Enquiry is so much earlier in its history, but I think a similar argument can be presented for it.) Therefore:
(1) We should recognize that the Sections both have an order and don't depend on that order -- every single one is capable of standing alone (in some sense), and, in fact, Sections X and XI are very difficult not to read exactly as if they stood alone. Because of this there is somewhat more license to dip into the ECHU and simply pick out a Section to consider on its own. Interpretation has to take into account what the other Sections say, but this is true of any collection of essays. This contrasts sharply with, say, the Treatise; Book I, Part 4 of the Treatise is not written so that it could be considered on its own, and who does not recognize the overall structure of Book I, and each Part of it, has radically failed to grasp some of the important features of Hume's argument. ECHU has a structure, but it is necessarily a looser structure. It's arguably designed so that the reader can take it entirely in more manageable bites, without having to hold massive amounts of the book in mind, which is the sort of feature that makes the Treatise much harder to read.
To be sure, Sections IV and V are not strictly stand-alone, but they weren't (strictly) stand-alone when they were explicitly called essays, either. One has only to look at typical essays of the period to see that sometimes we get not strictly stand-alone essays but essay-pairs and essay-series; likewise, one can have meta-essays that deal with points raised by several other essays. Taking it as a collection of essays doesn't mean the group has no structure -- it is also a unified Enquiry -- but that the contribution of the structure itself to the argument is relatively light.
(2) We should approach ECHU in terms of the literary features and style of the essayist. Section X is not a rigorous and grave treatise on miracles, for instance; it is an indirectly (but deliberately) humorous essay that uses Humean principles to turn tropes from Protestant anti-Catholic polemics ironically against Protestants as well as Catholics and practically blares in neon lights that it is doing so. It does raise serious and important points, but it deliberately does so with humor and elegance typical of the early modern essay. Section XI doesn't give us a rigorously philosophical discussion of particular providence; it gives us a literarily light essay of the sort you might have found in The Spectator, but uses this approach to give some discussion of serious philosophical arguments. And so forth.
These two features don't give us a radically different Hume -- people tend to approach several of the Sections in ways consistent with (1) already, they just don't usually do so for principled reasons -- although (2) does give us a lighter and friendlier David who is not trying in the ECHU to give a rigorous account of things (although this doesn't, of course, mean that he's necessarily sloppy) nor to give a fully serious discussion (although this doesn't, of course, mean that he doesn't raise a lot of serious points) but is instead putting serious philosophical ideas in a more popular and familiar form to make them accessible to the literate public. And that is very much in line with the way Hume describes his own project.
So in other words: I think the Enquiry is indeed properly read as a collection of essays, just like his other essays; although we should read this collection of essays as having a special unity of theme, purpose, and principle that is missing in the others. This latter point means we should in a sense take these essays more seriously than most of Hume's other essays because together they form a more strongly coherent philosophical project. And it's even possible that this is behind the re-titling, i.e., that Hume change the title to 'An Enquiry' in the hopes that it would lead people to take it as a substantive rather than merely occasional philosophical contribution the way most of his other essays are. In any case, that's how we should read it. But that doesn't mean that we shouldn't see it as a collection of essays; it means we should see it as a philosophically substantive collection of essays (on one topic).