...all of the best and brightest independent writers have already been booked solid as early as 3 months ago.

Whether it's a freelancer or writers at essay-companies, you're right about all of the best and brightest writers likely being "booked solid" for any 6-hour turnaround on 4,500 words; and nobody other than the best and brightest is even going to attempt such a project even with a full-day deadline. It's definitely the wrong time of year to expect anybody who's already busy making deadline after deadline to invest an hour or more just into figuring out a price to quote the customer for a project he might not even choose to order once he finds out the cost of meeting his deadline, assuming it's possible, which probably wouldn't have been the case on this particular deadline.
However, I've known only one other independent writer who regularly gets and maintains the volume of work that I do in this business and neither of us is ever likely to be "booked solid" three months in advance, even during our busiest seasons. Typically, we may have a few ongoing long-term dissertation projects that started a few months (or more) ago; but the vast majority or of our inquiries and booked projects almost always tend to be in the range of a couple of days before deadline to a couple of weeks, and
maybe one full month before deadline. Three months ago, trimesters hadn't even begun yet and even semesters were barely a few weeks old. The vast majority of our customers don't start looking for writers more than a month before their projects' due dates; in fact, most of them wait until the last week or two, or much later than that. A few days for this project could have been manageable, but he waited until a few
hours before his deadline for a project that was anything but straightforward.
The guy to whom you're responding isn't likely to have found any help from an essay company either, at least not without a deadline extension. As I explained, he first contacted me about 7 hours before his deadline for a complex 4,500-word project that would have required an hour or more just to figure out what it needed and what to charge for it, leaving only five or six hours of working time, assuming lightning-fast payment. Whether it's a freelance writer or an essay company involved, that process would have been substantially the same, because he couldn't even have known how many pages to order and pay for on his own; and at essay companies, the order would also have had to be processed and then posted onto their project boards before any writers could even have seen it. The automated order-processing system at the last company for which I did a lot of writing doesn't even accept deadlines shorter than 8 hours and from what I've seen on other companies' websites, they also limit the maximum length of projects that can be ordered for rush turnaround, however they define their "rush deadline" category.