However, Knowledge checks serve two important functions
Both of your functions essentially boil down to the same thing, using rules to bludgeon players or DMs into playing the game fairly and impartially. As we've discussed before, I don't feel it is appropriate to spend rules space and resources trying to force people to play "correctly." Either they will or they won't and the rules trying to force are just keeping the honest players honest.

Personally, the way I'd do it is give Fighters 1 bonus CS die every odd level, at the same time that Wizards gain new spell levels. Higher level combat maneuvers take up more CS dice to use (like an ability you get at level 19-20 takes all 10 dice to use, an ability you get at level 5 takes 3 dice to use), and you gain one maneuver each level. And then some abilities that are more powerful burn a CS die (either for the encounter or daily, depending on designer intents or the power level of the abilities).
So what would your progression look like? Something like this?

1: 1d6
2: 1d6
3: 2d6
4: 2d6
5: 3d8