There's really nothing a customer can do to guarantee that you'll get the writer you request from an essay company, because if companies
require writers to take specific orders, they're opening themselves up to claims by their writers that they're
employees with all of the employer-funded benefits and liabilities that come along with that rather than just independent contractors. The only thing customers can really do is specify that if their requested writer is unavailable, they want a refund instead of a different writer. If you specify that in your order, you can dispute the charge if the project is completed by a different writer. That won't get your project done by your requested writer; but at least you'll be entitled to a refund if someone else at the company botches your project. As an essay-company writer, I declined plenty of requests for me, simply because the project wasn't worth my time at the rate the company paid me for it. This happened fairly often after I completed a large rush project for a high price and the same client then started requesting me for tiny projects with long deadlines for which the essay company paid me half the per-page rate of the rush project.
Writers should consistently try to be available, especially if the client is a returning one who has a good record with the company.
I don't decline small projects like that for my direct clients. As an independent writer, I've gone way out of my way for good clients with emergencies, but even my independent clients still have much more of an obligation (especially, since it's for their degrees and in their personal interest) to contact me ASAP instead of procrastinating and burning off most of their deadlines in between getting the assignment and asking me for my help than any obligation I have to "consistently try to be available." I don't even know what that's supposed to mean. I have a schedule of projects on a filled-up project calendar and the rest of my life already revolves around my project deadlines. What else am I supposed to do? Never leave my apartment or ever do anything but sit by my computers when I'm not working just in case someone decides to contact me requesting a rush project? I already work very hard, but I have the same right as my clients to my own life when I'm not working; so a client's choice to wait until the last minute to contact me is just not my problem, even less so when it was an essay-company project.