Iirc, the whole point of restricting marriage was to eliminate familial nepotism & inheritance. A wealthy cardinal, for example, would then be forced to leave his estate to the Vatican instead of a wife or children. Likewise, it was supposed to stop titles being granted to the children of clergy.

Neither of these things worked, of course. A blatant example would be Pope Alexander IV, who had children via a mistress and still had the brass to promote his "bastard" to cardinal. The whole story is fucked up. "The Borgias" is a somewhat sensationalized and easy-to-digest version of events.