A problem I see with the skill system as it is right now, is that after reading a single chemistry textbook and cooking food for three days straight the PC has all the know-how to make methamphetamine.
This is silly and can be fixed, I think, by letting recipes call for both appropriate knowledge, and an appropriate skill.
IRL, making methamphetamine out of the back of a van with a chemistry set, in such purity that the reaction and it’s byproducts won’t poison you will require at least bachelor level knowledge of organic chemistry. At the same time a good amount of cooking skill is required to make sure you add, heat and stir the reactants fast enough without ruining the mix.
By having recipes ask for both appropriate skill and knowledge, helping that NPC doctor will be important because she can teach you about anatomy.
Knowledge can be quantified much like skills are now. On a scale from 1-10:
0 No knowledge
1-2 High school
3-4 College
5-6 Bachelor
7-8 Master
9 Doctorate
10 Post-doctorate
For obvious reasons one person can only teach another up to their own level of knowledge. Which means that once NPCs don’t suck they could ask you teach them.
Some very late-game actions, like restarting nuclear reactors or building nukes, should be dangerous (or outright impossible) without specialized knowledge like nuclear physics. (instead of the nebulous “computers” and ”electronics” skills.)
And once factions work properly, knowledge might become something richly sought after.
Those druggies might pay handsomely for anything you can teach them about making drugs, or the remnants of the military might want to know how to operate those [SPOILERIFFIC] weapons they found.
Knowledge can be more than just a check for whether or not a crafting recipe can be completed. It can be a source of income, a bargaining tool or a position of power among communities.