The counter question is this: Why gain promotion if all you want to do is train? If all one wants is a higher dan grade but does not want greater responsibility, then they have an ego issue in my opinion. If they are lazy and unmotivated as instructors, chances are that they do not enjoy or are perhaps miserable in the instructor's role. If their sole motivation is promotion, then they probably are not mature enough for the grades that they hold.
There are a great number of situations you are not covering. The choices aren't student or instructor. For example, my Grandmaster enjoys travelling round and helping different groups of people (sometimes with teaching them, sometimes promoting them). He also tries to help out on a national level with organisational/coaching.
He isn't interested though in running his own club. IMHO he has a valid reason for wanting high dan rank, and ego is nothing to do with it.
Not everyone's path is the same.
Yes, but that is not what Glenn said. He said that fourth dan and up is an instructor level rank. Nobody requires you to test for fourth dan. If you just want to keep on training, then nothing is stopping you from doing so as a third dan.
You say there's nothing to stop you staying a third dan, but there's also nothing coded in the Kukkiwon regulations about it being necessary to teach to obtain higher dan rank. Therefore, there's nothing to stop you from training up until 9th Dan without ever having had a personal student.
The Kukkiwon apparently realises there is success in multiple paths or the rules (like some other groups, e.g. the ATA as we have recently heard) would be different.
In and of itself, rank is unimportant. But it is not meaningless. The higher you go in dan grades, the more the emphasis is on giving back to and promoting the art. The primary way of giving back to and of promoting a martial art is to either open one's own school and teach or teach in a larger facility (thus facilitating the attendence of more students).
It sounds like you're advocating assistant instructors (the "or" after opening one's own school above) having higher dan rank than third? In which case surely this covers most people as most black belts assist in the teaching some of the time.
There is a reason that fourth dans can sign off on dan certificates.
I would argue the reason is that with the time you have spent (considering time requirements for each rank) training Taekwondo, that fourth dan is a reasonable point where you could be reasonably thought to be a decent judge of what each dan should be able to do/look like. I don't think it relates to whether you have your own club but a finger in the air "you've been doing it long enough, you can realistically judge what those below you do in terms of grade".
The reason is that they are assumed to be teaching their own students and either running their own or be on their way to running their own dojang. If that was not an explicit responsibility, the ability to promote students to dan grades would not be given
I would argue this is an implicit responsibility rather than explicit. The reason is that if it were an explicit responsibility to be teaching your own students that would be easily provable - how many Kukkiwon certificates have you applied for in the past x years since your last test.
Of course, many MNA wouldn't like that (as they don't like gradings outside the official association ones), but that would be an easy way for the Kukkiwon (or whoever) to judge whether you are running your own school.
My personal situation is that I have a rank above 3rd Dan but don't* have my own school. I'm an assistant instructor at my school and have been told in the past that I will be running the school when our instructor retires. Arguably therefore, I don't need higher than 3rd Dan. When the time comes though, I would then promote to 4th Dan so I could promote the students but I would be a lower rank than the club's competitors in the local area. Why does that seem sensible that I should remain 3rd Dan until that time?
* I have actually taken the decision to start my own club teaching children on a weekend now because I feel I'm at the stage of my life/Taekwondo career where I'd like to be passing on what I know to my own set of students. However, the above feelings remain true and I don't feel I should be restricted in rank until I have my own club.