And then there's Religious Settlements and Fertility Rights, which are broken because of the unit they give, but give a small, but nice little bonus all game as extra.
They're not though, especially not the builder.
The settler one is good, but it doesnt have what it takes to qualify as "broken" imo.
I'd define a "broken" pantheon as something that makes the game tremendously easier to play depending on whether you get it or not.
Not a bit easier, but tremendously easier
The settler imo does not qualify because its not an actually free settler, it increases the price for the next one, and adds the cost to one that you are currently producing, which can mess up construction timings.
With my particular opener I hardbuild two settlers anyway, and by the time I usually get my pantheon I am working on the second one and often close to finishing it before focusing on other things (usually setting up religion or invading the AI).
Now the adjacency pantheons, those are a different beast, because they frontload a huge benefit (assuming you get work ethic) for no real downside.
And the synergy you get with early war (crusade) yields a combo that is so strong that it can carry the entire game from the snowball it sets up, something a "free" settler doesnt do.
When starting around a lot of coast, „God of the Sea“ i choose always. +1 Production per fishing boat helps a lot for the way i‘m playing the game
That one I think is very bad.
I like it (for fun) on sea heavy maps, but its honestly a really bad pantheon in almost all cases.
The reason is that sea tiles early on are usually trash to work, even with a lighthouse active.
The bonus also requires a builder charge just for a single production boost, on a tile that usually doesnt get worthwhile to work until the mid to late game.
Heck, even if it frontloaded +1 production without requiring a fishing boat, I'd still rate it as rather bad, because that would take it up to a 2f/1p/1g tile, whereas what you really want is 2f/2p tiles or better (which you can usually settle and work for free).