So, really, why test? What does it mean to say 'I passed my ___ kyu or my ___ dan test, when the person with whom you train might not be able to tell, or might not care? Why do *you* test? What does your rank mean to you? What do you think it means to other people?
To say "I passed my n -- kyu/dan test" is to reduce Aikido to the status of one more qualification/certificate to be collected. Given that grades are not usually recognised between organisations and have a huge variance within large organisations (eg Aikikai or even individual clubs), it becomes meaningless to all but the gradee.
Personally, I test because when it happens, it happens. I have trained in places where the entire focus of every class was to practise the syllabus for the next grading and I have trained in places where there were no gradings -- students were put ‘under pressure' at unexpected moments and continually assessed during regular classes. Grades were handed out when the teachers considered it appropriate with a casual ‘you are now this, congratulations, carry on…'
To me, my rank is a measure of progress and it's just part of the personal relationship between student and teacher. To other people, I would suggest, it's pretty meaningless.
Gradings have become part of the ‘business' of the martial arts and a marketing tool to keep to keep the gentle masses interested, and paying.
Full consideration of the questions posed in the OP lead to more profound questions like:
What is the purpose of the martial arts?
Why do you train?