In fact, if Roddenberry and Barrett had wanted to cement her status as an important member of the crew, I think it would have made more sense for McCoy, when he was drafted, to have specifically requested her to be his head nurse, thus bringing them back together.
Interesting you should put it this way, because who's to say that's not what actually happened? We don't actually know
that Chapel was assigned to Enterprise
. She's part of the all-crew assembly on the recreation deck, but she may have come aboard due to orders issued by Kirk or Nogura rather than because Decker asked for her. If McCoy had a hand in bringing her back, he may have thought she was still a nurse and found out she'd finished medical school in his absence. That would explain his line to Kirk in the transporter room.