Okay so. Maybe the wiki I am reading is wrong. But it says their rulers get +1 to each stat. So when a lucky nation gets a 6/6/5 guy, that means they would have gotten a 5/5/4 guy. When they get a 5/5/5 guy that means they would have gotten a 4/4/4 guy.
When they would have gotten a 1/1/1 guy they instead get a 2/2/2 guy.
Although this is certainly. Like. A pretty big advantage. Especially over the long term. It doesn't seem huge to me. It's not like they always get impossibly good leaders. I mean, unless my source is wrong on that?
Just to put in perspective the actual difference, +1 to all stats will give the AI, assuming you play from the beginning to the end of the game's timeline, give it a total of 4514 more points
each for military, diplo, and admin. For 10 years, 120 points. It's a noticeable advantage both short and long term. Note, the beginning-end value might be a little off (I'm not sure if it applies the point bonus retroactively to starting rulers) but either way the points will be hovering around 4K even if an AI starts with a 20-year old ruler without the bonus that lives for 50 years.
Another thing to remember, is the Yearly Republican Tradition +1. Considering republics re-electing takes 10 Rep. Tradition, this means that Lucky republics can potentially
frequently get great doges. Heck, assuming one lives long enough, you could even see ones that reach the godlike 6/6/6 values. Granted, the AI isn't likely to make use of that as the chance of getting a republican AI isn't very high, but the point remains.