I've spoken to Snow Crystal about it, and looked over the code for how Rulership Focus works pretty extensively.
The problem, in essence, is that all of the opportunities from the Rulership Focus have a Weight Multiplier of 1, meaning that each has an average chance of firing once in about twentyfive years - and if you're at war, or part of a society or religion that has a lot of unique events, this is lowered further. The number of total events means you'll get about one rulership event every four years, not adjusted for the ones which fire more often under certain circumstances - if you have a Drunkard Vassal, if you have Feuding Vassals, etc.
So all in all, you only have a chance to get Stewardship bonuses from Rulership once every four years. No matter what, when you complete an opportunity, event 12500 (I believe is the correct id) fires, which has several possible outcomes - each of which has a 15% chance of firing (and luckily, two can even fire at once, so you can improve rulership, and gain a positive trait etc). There's a twofold problem that makes it so tough to get Administrator.
The first is that there are oodles of possible benefits to get. You can lose a poor trait or gain a good trait (and there are three total trait pairs that Rulership looks for - Slothful/Diligent, Arbitrary/Just, and Content/Ambitious). You can level up your Rulership (three levels, and the third level up will earn you the Administrator trait). And finally, if you have a Stewardship Education that is less than Midas Touched, you have a chance of leveling it up by one stage.
The second is that earning one of those possible benefits doesn't then increase the chance of getting the others. Already being Just, or Ambitious, or Diligent doesn't actually get you any closer to being an Administrator - the Focus has diminishing returns, so it's just genuinely not worth keeping for a long time unless you like the Stewardship Bonus. Each one always has a 15% chance of firing.
All in all, this means earning Administrator takes a very *very* long time. Your chance of getting it in just 12 years is about 0.3375% assuming one event pops every 4 years, and it is basically impossible to get it within the 5 years that would be typical to earn a Lifestyle Trait (except Hunter, another trait for which there's no way to speed up your earning time.) Someone more arithmetically skilled can do the math, but the number I've read is that it would take one character an average of 86 sustained years of using the Rulership Focus in order to get Administrator - longer than vast majority of character lifetimes.
For bonus points, see how many Random Nobles you have to invite before you see one who has the Administrator Trait. Randomly generated characters somehow have pretty good odds at just having something it would take a player character or even a normally generated character almost an 8th of a Charlemagne Start Game's Full Duration to earn.
EDIT: Did the math on this by think about Dice Probabilities. The odds of getting the Administrator Trait within the minimum number of rolls is about 1/296. The average number of events you'll need to get one Rulership Level increase is about 7. Since it takes about 4 years for one to pop during peace time, it'll take about 28 years to get one Rulership increase. Mutliplied by 3, it should take right around 84/85 years for one character to earn Administrator, and that's rounding down generously.