It's not as straightforward as all that. You have to remember that Starfleet isn't EXACTLY the military.
It appears that Starfleet Captains get to set the tone and control just who is on Senior Staff. Picard was Captain of the flagship, and he decided that he wanted a counselor to serve on his senior staff due to the likelihood and importance of diplomatic missions.
Picard was also a very cerebral guy. He was introspective and valued having a grasp on who and what he was; what his strengths and weaknesses were. He therefor elevated the importance of the ship's counselor to senior staff because it was something he, Picard, valued.
Imaginefor a minute you are on a science vessel doing deep space exploration. You might have a senior staff that included BOTh a Chief science officer and ALSO a chief astrometrics (or stellar cartography) officer because you have placed an added emphasis on science roles. That's both your call as captain, as well as the nature of your ship and her mission.
I doubt very much a senior staff has "MUST HAVE" positions. Maybe commonly held ones, but each captain probably can assemble their "team" as they see fit.
Look at Deep Space 9. They mentioned several times that there were several ship's counselors on board. You never saw them, because they weren't on senior staff. When Ezri Dax showed up (shudder), Sisko wanted to keep "Dax" as a team member, and suddenly chief counselor was on senior staff. He made the call as captain that his team would benefit from her.
Troi was practically a civilian. She didn't even wear a uniform until the last season, when suddenly a serious career in Starfleet appealed to her. Until that point, she was much more a mental and spiritual advisor. She didn't report to the CMO. She worked in conjunction with her in matters relating to the crew's mental health. In Beverly needed to pull rank, then yeah, up until the baloney promotion they gave Troi, she could have ordered her (Troi) to do something in a pinch.
Again, Starfleet is not the military. Things worked differently, and in some areas, more loosely.