Firstly, it's true that Chapel should really have been a junior doctor for the latter part of the 5-year mission and it isn't very realistic to expect her to become a CMO with so little experience. But since Ensign NuChekov was made Chief Engineer one year out of the Academy, maybe it's just me not understanding just how good humans are at learning in the 23d century.
I don't think the issue is whether it's better to be a doctor or a nurse - military nurses fulfill an extremely important role (as do other nurses). But story-wise it restricted Chapel's development as a character. I think it was a mistake to make her a medical doctor because it achieves almost nothing character-wise. She still, as has been observed, remains an appendage of McCoy. I think it would have made more sense to make her a PHD in bio-science and make her head of the Life Sciences department. While technically being a department that falls under the auspices of both Spock and McCoy, and while in TMP, the only thing that would have been different is McCoy's rant i.e. "I hear Chapels is a PHD now...", the character would at least have had a niche that could have been explored in novels.
I did love the air of authority that Majel bought to TMP compared to how drippy she was in TOS. I would have liked to see more of her in the subsequent movies. It's a shame that things soured a bit behind the scenes.
I wrote a little comic story for Youtube and tried to use Chapel as the more scientific doctor compared to McCoy's 'old country doctor' but they do eat into each others' screen time.