Can we build the math from the ground up? (And does Vancian help or hurt that?)

[Kyutaru]

It's usually very one-sided in most RPGs, as the ratio of Violence-to-Nonviolence features aren't usually equal, and Nonviolence features can often have their own value in regards to combat, whether it means pacifying a threat, preventing a fight from ever being necessary, or even providing its own means of contribution.

Instead of that being the RPG's fault I find it usually is the result of the perceptions of the participants. Combat and the rule mechanics are well defined and the crunch is frequently discussed. But noncombat fluff remains subjective to each table and doesn't get outlined as well as the violent stuff. That's not to say that nonviolence isn't equal, I've had games where it was more important than the violence, but that people take the rules light approach to infer that. It's very much not the case as past editions tried a heavy-handed approach to controlling the roleplay and narrative. This backfired and was poorly received while limiting content creators. If players want to sit around and roleplay as the Vampire court, very little combat will be happening. But if players want to throw themselves head first into the Den of Vipers then expect to make a lot of attack rolls. It all comes down to the theme the table is comfortable with and in a crunch-heavy game in a world of video games there will be quite a few combatants drawn by the prospects of rolling to murder.

Consider how often an Illusion is usable out of combat. Then consider how it might assist or prevent combat. Then consider the same for Grappling. How can those be even?

I don't think everything can or should be equal. But while illusions cannot stop someone from climbing the tower, a grappler very much can. Different roles don't mean one if less useful as that depends on how often the grapple opportunities come up versus the illusion ones -- which is very DM dependent.

Then do the same for something like Detect Thoughts vs. Super Strength.

Good Cop, Bad Cop. Sure, you can plant a bug in their car and try to listen in hoping to hear what you need for a conviction. Or you can just put me in a room alone with them for five minutes.

If there's only going to be one fight every 3 sessions, you're going to feel really stupid picking the class that's 90% violence and 10% nonviolence. Unless you can ensure the character that is the inverse of the Violence character has only a 10% violence capacity, there's not going to be a level playing field.

Yep, which is why DMs have to work with their players to determine what will be fun for everyone. It's like giving players a dungeon full of traps when no one in the party is a rogue. They're not going to have fun.

Consider that the Wizards of DnD have always had some capacity for killing things, and also have capacity for manipulating the world (using strictly Wizard features), and that the same has not been true for something like the Fighter. Generally, if the Fighter is successful in this area, it's for reasons despite the class, not because of them. Effectively, Violent characters are often handicapped in noncombat situations, and the opposite hasn't had much history of being true.

The Fighter's way of "manipulating the world" was generally through Leadership and minions. For some reason all the caster disadvantages like casting times, interruption, low health, a weakness to gags and manacles, and a single spell cast per round have been eliminated while martials have lost some of the only features that made them worth a damn in 2nd edition.