Just sort of playing devil's advocate here, but wouldn't that depend also on the 'consequences' of failing, even (or perhaps especially) the psychological consequences? I wonder if failure was _very very_ common, if there might actually be less fear of failure because 'it's no big deal, it happens to everyone all the time'? I don't know if that would actually be the case (or maybe if might just shift it from 'fear of failure' to 'really hoping you can pass' and make passing that much more exciting and rewarding, which could be a motivator too), but I do think if failure is a minority but possible if it makes you really not want to be 'that one that everyone will remember who failed' or however you may picture it in your mind.
In any case to me personally it's more important mainly to 'know that I really honestly passed', so I would just be suspicious if testing and grading seemed too automatic or arbitrary.
Good point. Probably the ideal failure rate from the perspective of increasing the stakes psychologically is around 10%. This is enough that people know that there is a real possibility of failure but not so much that failure is too commonplace. It's kind of like a casino (expect in reverse): they need to let you win sometimes to keep you coming back, but not enough that they would lose money.
In the case of aikido, there's also other good reasons why they want to keep the failure rate low, beyond the fact that it becomes more of a stigma to fail. Because rank is so tied to status in aikido dojos, failing a rank test can be a major blow psychologically not just for the failure but also for the consequences in daily training, so they need to be judicious about using it. In competitive arts like kendo there are other formal provisions (such as tournaments) for the expression of physical skill in ways that give practitioners a socially-acknowledged feeling of accomplishment. In aikido, often even informal expressions of skill in paired practice are only permitted in ways that correspond directly with rank, if at all. So rank takes on an elevated level of importance in aikido and it becomes a much bigger deal to formally deny it to someone.