Something happened in the centuries following, though. You can catch a glimpse of it in the changing livery of the essay's prepositional outriders. In English, the earliest essays (e.g. Bacon's own, and John Florio's translations of Montaigne), tended to have the word "Of" at the beginning: "Of Praise", "Of Followers and Friends", "Of the Education of Children", and so on. "Of" was a subject marker, but one that suggesting that the writer was partaking of the subject without entirely clearing the plate.
In philosophical and scientific circles, at some point in the seventeenth century, the word "towards" seems to have become popular. Hence John Wilkins' "An essay towards a real character and a philosophical language" (1668), Berkeley's "An Essay towards a New Theory of Vision" (1709), or Bayes' "An Essay towards Solving a Problem in the Doctrine of Chances" (1763). I approve this choice: it suggests that the essay isn't a finished form but a vector, a movement in the direction of knowledge, a baton passed to futurity. It sits well with the conception of knowledge as a collective enterprise in which no one person can hope to achieve all.
After a while, though, this was superseded in popularity by "on". I suppose Pope may have had something to do with popularising it; at any rate, we can cite "An Essay on Criticism" (1709) as an early locus classicus. There's something closed off and uninviting about this preposition, something that descends on its subject as if from a great height. It seems to fold its arms and say, "Beat that, if you can!" It's a preposition for a more individualistic age, perhaps, but I can't help thinking that it stimulates further argument, if at all, in an unhelpfully adversarial (or at least emulous) way.
So I say, let's bring back the tentative nature of the essay! Let's leave its loose threads hanging instead of tucking them into the hems! Let's detach, as far as possible, arguments from egos! And let's listen to Bacon's sage advice in The Advancement of Learning and apply it to the essay form:
Another error... is the over early and peremptory reduction of knowledge into arts and methods; from which time commonly sciences receive small or no augmentation. But as young men, when they knit and shape perfectly, do seldom grow to a further stature; so knowledge, while it is in aphorisms and observations, it is in growth: but when it once is comprehended in exact methods, it may perchance be further polished and illustrate and accommodated for use and practice; but it increaseth no more in bulk and substance.
I would write a polished conclusion at this point, but it seems against the spirit of the post.