In my games Celestial Exalts do not have empowered children; not godbloods, not gods-in-flesh, not anything. The child of a Solar is a mortal. The Celestial Exaltation was designed explicitly to prevent two things: immortality and dynasty creation. Regardless of how awesome your Essence or mighty your Charms, eventually a Celestial dies and their children are normal children like anyone else. This was things working as intended. The Incarna knew they had to do something with the Celestials after the War, and they did not want immortal empires of Exalts looking hungrily at heaven.
That being said, often the progeny of Exalts had powers and abilities beyond mortal ken but this was because such children were the… let’s say ‘beneficiaries’ of Celestial-tier Training effects, sorcerous imbuements, biomotonic induced mutations, Enlightenment effects and everything else the parents could hit them with. Quite a few of them were promoted into gods as well after certain Zeniths and Eclipses called in owed favors.
As a Celestial Exalt, if you want to turn your infant into an inhuman being you have to work for it. The Golden Children were not an accident of birth, they were a deliberate and ongoing effort by the Deliberative to supplant the Gens with a less powerful but more pliable and loyal middle class. After all, the prevailing wisdom was that Dragonblooded were defunct. The systems crafted by the Solars were so perfect they did not require Dragonblooded most of the time, and the few occasions they did a single Solar troubleshooting for a month was often worth more than a hundred Dragonblooded working round the clock for years.
As for Abyssals and Infernals? Abyssals can have children, all the children they want. The problem is that doing so causes a shit ton of resonance and the resulting resonance backlash is likely to be bad for you and the child. Infernals can have mortal children unless they invest heavily in certain Yozi (Kimbery, Metagaos, Adorjan being the big ones) that allow you to have fucked up monster children.
(Also, any ruleset which prevents me from running the dispossessed child of an Elder Exalt recruited through contrivances into a faction that opposes them is a bad ruleset. If the daughter of my Solar warlord can not be a crushing failure and disappointment to her mother such that she gets offered an Infernal Exaltation then nope, not going to use it.)