Keep in mind that "falsifiability" is not a scientific concept, it is a philosophy-of-science concept. Specifically, Popper articulated the concept in order to divide Science from pseudo-scientific theories masquerading as scientific. In other words, Popper was worried that theories like Marxist History and Freudian Psychology were latching on to the halo effect and portraying themselves as worthy of the same serious consideration as Science without actually being scientific.

Thus, there's no particular reason to desire that a belief be falsifiable. Popper's project was simply to define Science such that only falsifiable statements and theories qualified. It turns out that scientific theories are much better at making future predictions than non-scientific theories, and we have philosophy-of-science reasons why we think this is so. But falsifiability is a definition to clarify thought, not a virtue to be aspired towards.