It isn't unsurprising that this story would leave out the whole "Olympians are all wizards who like Zatanna can do whatever the fuck they want" aspect from the comics considering all the New God buffing in this story.
Rather hard to take New Gods seriously when the Olympians are infinitely more versatile.
In fairness the New Gods in the comics have been portrayed as being powerful enough that the ones we see are just avatars of some multidimensional entity, or sometimes they've been shown as being weak enough that an ordinary human can beat them.
Darkseid was once beaten by a couple of thugs.
We've also not seen as much of the Old Gods in this story compared to what we've seen of the New God's, so it may be difficult to accurately judge how they compare to each other.
I'm fairly sure that Old Gods are at least as powerful as New Gods in this story, though they may find it difficult to bring their full power to bear in the material universe seeing as they're more energy beings that can take on a human form, but due to their incompatability with the material universe they can't manifest their full power, while New Gods are more like superpowerful demigods, that being physical beings with highly powerful magic and souls, so find it easier to bring their full to bear.
Old Gods probably are more versatile than New Gods, but that doesn't mean that they don't tend to prefer using their Domain powers over other magics.
In the comics Darkseid and Ares once manipulated Zeus so that he may fight Izaya and Izaya thought that they could both kill each other if it came to a fight.
Izaya is basically Darkseids equal and he thought that if he fought Zeus that Zeus could kill him.
So if Zoat decides to use a similar power level for his stories version of Zeus, then I don't think he really nerfed them all that much.
You gotta remember, Paul is really bad at being an actual leader.
And you gotta remember that so far Paul has shown himself to be a competent leader when he took up such a position.
The same goes for most of his other versions who took up leadership positions.
He's not perfect, but he's also not exactly the flailing infant you seem to believe he is when it comes to leadership.
Case in point.
Leaders are always needed, if only to read over and sign the endless amounts of paperwork that cross their desk.
There is such a thing as delegation.
His role is also a whole lot more ceremonial now with his wife running the actual day to day government, along with whoever works below her.
He most likely trusts her and that warrior cat that hated Lion O to run things competently, while others either respect or fear him to not step out of line.
He also created a government that won't have to rely on him to do everything since when Krona took him it could have spelled the end of whatever he built if he was absent and made a civilization that relies on one guy for everything.