FreelanceWriter - is the only real deterrent from a half-now/half-later payment plan (on a relatively short essay) that scammers might get involved?

Not at all. Generally,
most clients would probably pay after the fact without a problem. However, we cannot afford to absorb the loss or waste time chasing down payments for even a few clients who don't pay up immediately or to make a living getting paid without an issue only "most" of the time. This work is stressful enough with constant overlapping deadlines practically every working day of your life without also having to worry about whether you're even going to get paid for work you just stayed up all night writing or cancelled your non-work plans to squeeze in for someone. Getting stiffed on a payment is also psychologically demoralizing and keeping track of all your deadlines is already enough of a headache without adding more work to keep track of who owes what for work already delivered. Prospective clients at least have some ways to "vet" a new writer who's been in this business for any length of time; as a writer, you can't check out the student the same way and it would waste too much time even if you could.
Furthermore, anybody who's done this for a living for any length of time (whether freelance or for companies) has encountered occasional demands for revisions that are totally ridiculous. For example, demands to add or remove biographical information about a psychological theorist after the work has already been delivered when the only specs were "5 pages on Freud and his theories." If it hasn't been paid, payment can be wrongfully withheld to leverage free revisions that are not fairly owed. Same goes for requests to revise (again, after delivery) based on conversations between the client and the professor occurring after your work was already delivered days earlier, exactly as promised and meeting the specs provided at the time it was ordered. All of that extra work can certainly be negotiated fairly, but if the client hasn't yet paid, you could be fighting just to get what's already owed for your work.
Secondly, is there any harm in providing updates/drafts on such a small piece, especially if the client is willing to pay for it?
None at all, but usually, they are not "willing to pay for it" (or
expecting to pay for it as something extra) when they ask that way. Usually, they just have a very unrealistic student's-eye view of the writing process and imagine that it takes us multiple sittings spread across a week to produce a 5 or 10-page paper. They also don't necessarily realize that their project might be one of a dozen or two-dozen or more projects on your calendar that week or two and that it's not as much on your mind as it is on theirs for that entire time. If they offer to pay for your time or if you're only dabbling in this as a writer and have only one or two projects pending in a given week, I suppose it's totally up to you if you want to engage in a prolonged email exchange and/or multiple phone calls to discuss a project that you really need no assistance to write and about which you have absolutely no questions requiring answers. Typically, you'll be responding to college freshmen wanting to "discuss" points about writing that they've just heard for the first time from their professors that week but that no professional writer needs to spend time discussing, especially for some 5-pg paper that you plan on banging out in an hour or two next week on the day it's scheduled on your calendar to be written and that will probably be an "A" in quality without any discussions about it after you confirm that you have everything you need for it.