I don't really see the point. I rather pay for teaching that helps me to improve than for someone selling me a document which doesn't help me to beat this particular guy in the go club. Or is it that regular payment as a kind of endorsement / sponsorship is still somewhat odious so paying for a rank certificate is a more polite / acceptable to the same end for both? (I don't believe the notion that the buyers are fooled in the process. If they play at all they can very well measure their progress themselves.)

Of course they are not fooled. They want to show off.

I think most professionals make their money from teaching in Japan, not from certificates. However, the certificates are probably a way to keep students interested and paying for lessons. We used to use the same techniques when I was an English teacher for a company here in a corporate environment. If a student was stagnating, we would "fix" the test/assessment so they could progress to the next level only when the sales people told us it was necessary. When I say "fix" it, I just mean that we would ask a particular teacher to administer the test. This teacher was usually the most kind and lenient of the instructors, so that they would pass the person. After passing the test, the person would usually buy a big block of new lessons, so the sales staff were happy and we could all continue working at our jobs.

My guess is that the same technique is being used by Japanese go teachers. If a students is not progressing, they will issue certificates anyway when they seem to be ready to quit. This gives them new motivation to continue lessons and pay the instructor.