So the short of it is that with knowledge, you get better everything else. You get better traits, which makes vassals like you more and disencourages murder / rebellions. The more you're liked, the more troops you get. In addition, the quicker you can upgrade your military units and get more men at arms. It improves development quickly, and development is where your taxation is based, so you get more money. It makes the church like you, and makes converting counties to your religion / getting a claim much faster; this also helps getting money from the Pope if you're Catholic/Insular.
I guess the only thing it doesn't really improve is intrigue, but the truth of the matter is you don't need high intrigue to be successful.
It also makes your ruler live longer, which is /huge/, and you know 1 year before he dies. There's no surprises (because everyone loves you, you're not likely to get murdered -- and you have money to improve their opinion). Your ruler can live, in medieval terms, to 70-80 yrs old, whereas if you focused on anything else, he could drop dead at 40.
