I just realized that I have a sole exception to Hera x Percy ship. STAY WITH ME NOW.
We all know how lustful Zeus is, Hera is almost fading away from the broken marriage but notices the way her husband looks at the first female hero of Olympus.
Young Percy with her sharp tongue keeps saying 'no' and runs away from him. Hera is pleased, after two thousand years of bad reputation and she keeps coming back to Hera.
Maybe it's because she's been submitted for so long but Hera remembers how wild she used to be before patriarchy existed.
She's the queen by birth title, not Zeus. Hera appears in Percy's dreams, she tells her to convince Zeus to marry and, in the altar instead of swearing loyalty to "Our marriage" she could swear to "The marriage."
A loophole, the plan goes surprisingly well. They play as rivals but in reality they are counting down the days to be together. Not for love, but for something more deep in a religion without marriage and loyalty engraved.
In the altar, after Zeus forcefully takes Percy she swears loyalty to "THE marriage", a slight difference that changes everything.
It gets better if you think of the first night, Zeus dragging Percy into the master bedroom, the one for queens and kings, and finding that only Percy can enter.
His lust slowly wears off, only to find Hera inside the royal chamber.
She never took off her crown, and since she's in a new marriage no one can take her title as queen. Even worse, Poseidon gave his daughter a little bit of his fertility domain, Hera is now with a wife that can bear her children with a strong alliance to Atlantis and free to have lovers as much as she lets her wife. (Equity in marriage is one domain that is born after this.)
Percy cares for the demigods, has her lovers (except when preggo) but every night she goes back to the royal chambers.
Hera re-does the whole Olympus solely based on connections. Minor gods get to form an alliance based on similarities on domains, change of representatives every year.
The twelve Gods get to stay in their places but they must stick to their original domains and not expectations of their domains.
No more weird punishments like Dionysus or Apollo, instead she lets them prove their innocence.
And as a marriage of equity, that does whatever they please and whoever they please. The only rule is to always be loyal. No need of fidelity, only loyalty.
They're both birds of a feather.