I would hope, but know it is not the case, that anyone beyond 2nd Dan in any art, is there because their Sensei/Soke/Head of Family/Style/etc, has made sure that they can teach, AND that they know the art's technicques, philosophy, etc.
Let's go back to the Menkyo system, pre-dating the belt system. A "Master Instructor" (for lack of better word for now) taught their art to his (or in rare cases her) students, and when the Master felt that the student knew the content of the art, the philosophy (and I use that term to represent the reasons behind the moves, why they are done that way, why those moves and not others, etc) behind the art, he gave the student a paper authorizing him to help teach the art under his tutelage. When the student got better at teaching and was considered to FULLY know the art and was FULLY able to teach the art, (s)he was given a "full transition of the art" paper which allowed him/her to teach it to whomever they wanted. (Semi gross review of the process, bit more to it, but covers the basics.)
Now, let's transition that to the belt system, as originally intended by Kano (per his writings) and initially used by early adapters, and some still: (And I posted this before, but too lazy to go dig up the link.)
1st Dan: Has the basics of the art in hand, a bit more learning, starting to teach (now many schools start the teaching at brown or before, I'm not for that though, they should be dedicating their time to learning and improving, and watching teaching by others) under supervision.
2nd Dan: The training of new things is done, and the person is given permission to teach, still under the tutelage of their Sensei, but does not require 100% supervision.
3rd Dan: The person is now given the ability to teach on their own, and can advance students on their own.
4th and 5th Dan: Achieved with time, dedication to the arts, and teaching students and advancing students to Dan rank.
A black belt, to me, implies that the person knows the content of the art (or most of it in the case of 1st Dan), has been "tested" in the teaching of the art and can demonstrate the art to students in such a way that it works for the student to learn the art.
If a person is not able to teach the art, doesn't fully know the art, why do they even want a "Dan" level rank in the art?
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So, to answer your question, I, assuming I find a school that has these standards, would want to be learning under someone that is at least 2nd Dan, and would prefer not studying under a "Kyu' level student. In the 40, almost 41, years I have been training and studying the arts I have been in, I have noticed MANY Kyu level "instructors" and in a vast majority of those times have noticed that "instructor" teaching the concept behind the move or the move wrong. This is bad for the student, the instructor, the school, the head "Sensei", and the art. For that manner, because of the lack of structure to the belting system these days within an art or style, I have notice many 1st, 2nd and 3rd Dans teach their art (and I'm only limiting myself here to arts I have trained in, and am only guessing from what I have learned in other arts from reading, talking to "Masters", etc...) incorrectly or without knowing what they are saying.... Not good.
**** Disclaimer: In many of the systems out there now, these standards are not met, and belts mean less than they should mean. Now to know if you should train under a person takes you watching what they are doing, listening to what they are saying, and asking about their training, what they were taught, etc. Knowing more about their Sensei and the style requirements is important too. Unfortunately many new students coming to a school don't have the knowledge to know if what they are getting into is the way to go. (And us on this board telling people to go check out the school and see if it works for them is kinda counter productive in this scenario. How are they going to know if it is good or bad if they have no clue about the arts, that style, etc?)*** (/Rant too...)