In your scenario, imagine if the first nurse had it drilled into her that she must tick a box on the patient checklist, which lies very visible next to the patient and is almost impossible to not notice, and you have a physical system that makes it difficult to commit mistakes
I haven't had any problems of this scale, but my doctor can't even schedule a follow-up appointment 3 months in advance.
They can't even use a calendar, much less a checklist.
My pills are prescribed for 3 months and they always manage to hem and haw and almost miss the window as if the passage of time was a recent concept that their practice was unequipped to deal with.
On the other hand, every psychiatrist I've ever had, had no problem getting my anti-psychotics or anti-ADHD medications sent to the pharmacy inside of a day.
Psychiatrists seem to operate out of groups more often (I see far fewer solo psychiatrists). Groups mean that you have to have EHR software that works well enough to transfer patients between doctors, and you have to have standards set up to where doctors can read patient histories from other doctors. Basically your EHR system needs to be functional, which has nice side effects like making scheduling and prescription refills work correctly.