Which is quite difficult to obtain cause you need a level 3 statesman and a good monarch I think. Also it is available for the second half of the game, while lack of piety and islamic center (to a lesser extent) are available always.
oh no, its incredibly easy. Firstly you don't need a statesmen iirc. All sunni (maybe even all islamic?) nations can enact 3 different decisions if a monarch has any stat 5 or above, its learning center for adm. I forget the others, i think adopt title of kalifa is the mil one. You can usually kill off bad heirs via events or marching them repeatedly into losing battles. If I get a bad heir (low adm skill) I actively try to kill them constantly. It seems like once you get a good breed of rulers, they continue for awhile, maybe not all of them 5, but still, that is only 5%, you could still get massive discounts with islam.
In my aztec game I have done similar, monctezuma is a pretty good ruler, killed off my first heir, got a new (low legitimacy) heir but he had 5/4/3, took awhile but next heir was 4/4/2, but before he even took the throne, I got a regency 3/4/2, then the next heir was 5/0/6. There is some luck involved obviously, but it seems like the game rewards you somehow once you get it going in the right direction. I have earned stability via raise our prestige mission, and on a few random events plus I never enacted divination, but I did enact religious sacrifices and rite of passage, giving me a total 35% discount on stability. I think I might have a chance lol.