Most GPs won't write you a scrip for ADHD medication on a whim, either, but I wouldn't describe Vyvanse as "illicit." They just "know what they don't know" and so don't trust their own evaluation of you and think you should get a professional evaluation by a specialist (i.e. a psychiatrist, in this case.)
They're usually perfectly willing to continue prescribing after you've gotten a previous scrip from a psychiatrist, though. I suspect ketamine would be much the same, except that you'd need to get your scrip filled at the pharmacy of an inpatient hospital (since that's where they'd have it in stock), rather than the corner store.
It's the same story as, say, methamphetamine. Scheduled drug—but that doesn't mean you can't just get a prescription and get it filled. It's a lot of work to get that prescription (since methamphetamine is also a last-line treatment), but once you have it, any hospital pharmacy should have some in stock.