Gensokyo and its residents, such as the many youkai, gods, and other entities, share some similar behaviors with humans. There is always the possibility of another incident occurring, whether it be another invasion from hell, the moon, or some other place, or simply another enormous change in the existence of Gensokyo, like the awakening of the Saigyo Ayakashi. With residents or entities that have access to Gensokyo and the power to create, obliterate, and destroy life, worlds, as well as the rules and borders of reality and physics, it would be wise to keep the Hakurei kami hidden as much as possible. With entities that are immortal in a world subjected to constant change, honor, and boredom for those to whom it applies, it would only be a matter of time, not probability, for the Hakurei kami shrine to be attacked, as it is one of the fundamental principles of the existence of Gensokyo. Keeping the powers and rituals hidden from everyone except those who rely on its power is an integral and safe way to ensure that future and potential enemies of the Hakurei kami and its allies do not know how to strike and attack them at their core. It would be akin to striking not in the darkness of a forest, but in a vast vacuum where you fall into. There is clearly something where your presence is felt and moving, yet there is nothing to hold onto, recognize, or affect.
The Hakurei kami is powerful enough to maintain its authority, as demonstrated by the effectiveness of Reimu's abilities and power. Despite claims that the Hakurei kami does not receive enough faith, Reimu was able to defeat Kanako Yasaka and Suwako Moriya, who were two gods with enough faith to have physical embodiments, in contrast to the Hakurei kami.
But as stated by Byakuren Hijiri, the Hakurei kami is very angry that it is not worshipped because Reimu rather "hunt youkai all the time" instead of taking her buisness at the shrine more seriously. so maybe not all goals of the Hakurei kami and it's allies are met or fullfilled and it can't actually peform certain actions or materialize or make certain information and goals clear. It could also be that the Hakurei kami does have enough fait, but chooses or is forced to prioritize it differently, making the Hakurei kami unable to materialize but giving Reimu immense power when needed.
In a Gensokyo subjected to constant changes, incidents, powers, and problems, the best way for controlling parties to guarantee safety is to focus on being effective rather than following "rules" and traditions as others do. Being a somehwhat controlling factor from above. And so far, it has worked for the Hakurei kami, its shrine, its allies and its miko's.
