Just as Lin Xiao's school only handed out a few cards at the end of every academic year, which were far from enough to go around, only the most outstanding few students had the chance to snatch them up.
Although the descendants of True Gods didn't necessarily lack Divinity, possessing Divinity didn't mean it could be integrated randomly.
It's known that Divinity not condensed through one's own Power of Faith is impure. Moreover, Divinity doesn't appear out of nowhere; it accumulates through the condensation of the Power of Faith provided by the followers of other Demigods or True Gods. Naturally, it contains a plethora of the spirits of different believers, as well as the condenser's own spiritual Branding.
To fully integrate it into oneself, one had to spend time completely refining the spiritual Branding within. Otherwise, influenced by the different spirits within the Divinity, at best it could affect one's personality, at worst it could limit one's potential.