According to a piano teacher, the initial grade is a great motivation to the student in the learning.
I have to admit, I will only put a student through exams if I know (or strongly suspect) they will do well in them - that is pass. And then my goal is to get them to a point where they will achieve highly.
So to a point, I agree with the statement that the initial grade (and ANY grade they first take on) is great motivation. However, only to a certain type of student.
I wouldn't for instance encourage a student to do exams if they hardly ever practised,if they missed lessons (whether or not it's their fault or the fault of their parents), if they were also struggling with school.
I have encouraged students to do exams who aren't putting in an awful lot of effort in the lesson or at home, because I've seen their aptitude, or how quickly they can pick up concepts, or that when they do play, they have a certain musicality, or something else that I've picked up.
I did this just recently with a girl who would HO HUM through the lesson, roll her eyes, do minimal practise, but played extrememly well for the little effort she put in. It was a bit of a difficult thing to convince her and her mother that the exams were worth it (and we're not talking money - they have that in abundance).
She just sat for her first exam only a few weeks ago and did exceptionally well. More importantly, she is now consistenly the top practiser in my studio, has recently bought a piano (instead of a keyboard) and says she wants to do exams up to grade 8. When she first started, she said she was only going to have lessons for another two years. Her love for music has grown tremendously in just that one year.
it gives good exposure to the students.
"Good" exposure for what? Do you mean to prepare them for the NEXT exam? Any first exam will do that. And again, I don't think it's necessary to 'expose' all kids to the exam system. I had one student whose mother INSISTED she do her first exam (only because her older sister was doing so well in them, and she had a friend who her mother was competitive with

). I had said very firmly NO one year and explained why. She came back the next year and explained why her child needed to do the exams. She mentioned motivation. (Again, it was only to 'keep up with the Joneses'). Same woman was paying her child to practise. When I put a stop to that, the exam idea came up.
Anyway to cut a long story short, I agreed to put her through exams, did the paper work, she paid me, got the confirmation back and then she announced, "No, it's too much pressure for her, I want my money back." Two weeks later the girl quit lessons all together. (Older sister is still going and doing very well in the exam system).
I didn't want to put this kid through exams in the first place because she was a very shy girl who even found it difficult talking to me, had a short attention span, was happiest when only copying me rather than working hard (had two other teachers before me who taught that way).
then how to judge or know that the student is up to certain level?
I guess through experience. I don't teach using any particular 'method' as such. I assign pieces according to difficulty, teach theory as it arises, (although I also have a separate group theory class I invite certain ones into) introduce scales and technical exercises as needed. I also like to to composition, arrangement and improvisation.
Because I'm very familiar with the grading system (because I do put students through exams) I can judge what a particular student's 'level' would be. But I don't go around telling them, "Well you're about a grade three standard, you're definitely grade 5" etc. They just play the piano!