Do you disagree that it is not rational to hold beliefs with no predictive power?

Well, I did yesterday. What I mean is, I sat with that idea for a while and believed it the extent that it was convincing, but now I would like to challenge/test it more carefully.

So right now I am considering the hypothesis that it makes no difference to being rational if you hold certain beliefs, if they hold no predictive power.

I always feel uncomfortable with anything relying on Occam's Razor: Occam's Razor is meant to indicate the probability of something, it doesn't have the power to decide things one way or the other. (For example the probability of picking a number from an infinite set is 0 -- not close to 0, but actually 0 -- but that doesn't mean it would be impossible to pick a number from an infinite set if there was such a thing as an infinite set. I'm just not sure.)

What convinced me before, instead, was the argument that if there is no reason to believe something, then it is irrational to unnecessarily assume it. Now I am wondering if there could be any harm in doing so.