The importance of philosophy in the question of what we believe

Hello Rabbi,
The rabbi was very concerned with proving God and giving the Torah. The question arises – what is the importance of this?
On the one hand, if we say that a person should believe precisely for the right reason and therefore it is important to know why we believe, what about Maimonides and the medieval rabbis who believed on the basis of philosophical proofs that seem to us today to be wrong, or at least not very accurate? What about the sages who apparently did not deal with the philosophical reason for belief at all?
On the other hand, if we say that this question has no importance from the point of view of faith itself, what is the importance of explaining philosophically why we believe in God? Is it merely a tool of persuasion for people who have doubts about faith?