I always viewed the Godless as a significantly weaker faction than those of the major Gods. They only have a fraction of the resources and manpower of most of the major gods. With the exception of Vorago and the Guardians of Guthix (maybe), the faction doesn't have any heavy hitters that can go toe to toe with the gods themselves or the factions' elite troops.
The main reason why they still exist is because they're not really noticed by the Gods. To most factions, they're just a bunch of ill equipped fools with little to no impact on their war effort. The best that the Godless can do is sabotage factions repeatedly, like a more benevolent version of Bandos. I don't have a doubt that if any of the major gods decreed that the Godless had to be exterminated, the Godless would lose the fight relatively quickly.
I'm not sure if Anima gives them that much of an edge in combat as everybody else thinks. All major god factions have humans in them. I don't doubt that if they wanted to, the gods can weaponize anima for their followers.