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Let's instead look at the number of skills with Intelligence included. For all those other caster types I'm assuming an Int of 10, because they're all in need of Dex, Con, Wis and Cha. Also, all of the classes also get one more skill from Backgrounds.
Wizard: 8
Witch: 9
Alchemist: 9
Inventor: 9 (or less, the class also wants physical stats because it's a weapon-user).
Investigator: 11Sorcerer: 6
Bard: 7
Cleric: 5
Druid: 5
Oracle: 6Now, of course these other casters could pick up some more skills. But it's somewhere in the lower tiers of priorities for them. Meanwhile, wizards are pretty much guaranteed to take that Int 18.
Witches get a little more (but people constantly complain about witches being weak), alchemists might focus later ability boosts and apex item at Dex instead, inventors are still very much in playtest. Investigators stick out, but investigators are supposed to excel as a skill monkey class. Even so, the difference between 8 and 11 isn't really as big as the difference between 3+ and 6+ made it look
I'm not sure that this makes the point you think it does. You're still looking at an unexplained structural inequality with the design of the Wizard, which runs counter to that of other Int based classes.
Assigning stats or notif build paths to justify it is just making Just-So explanations that don't hold any real value. A Wizard, for what ever reason, might not have Int as their primary stat, or an Alchemist may indeed go whole-hog on Int, in either case these Just-So explanations break down.
Whatever way you look at it, we're still left with a Wizard chassis that has worse profiences, less skills and less (+ worse) focus spells than other classes in its mold. We known it's not a 4 slot caster issue, as none of these are present in the Sorcerer, we know its not a prepared or arcane caster issue, as none of these are present in the Witch. It just seems to be unique design penalties to the Wizard with no real payoff elsewhere in the chassis.

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Recommendation Updates:
Armor Proficiency is 1, 2, 3, 5 for Unarmored, Light, Medium, Heavy
- I took the advice to lessen importance on armor, but I already gave this core function a really low factor anyway. It's hard to lower it any further, and I keep coming back to: Armor Prof. gives you the option to put points in something besides Dex. Dumping dex with Heavy armor prof lets you give your martial better Cha for Intimidation/Social or better Wis for Will Saves. Those are strong options. I can't see dropping armor any lower than its already low 1-5 range without losing that representation.
Barbarian, Bard, Champion corrected for Save Shifts and Greater Weapon Spec.
All Classes' Saves updated Legendary Save Points to be 6 instead 7. Updated Save Shifts to be 3 points instead of 4 and also added 3 points to Save Shifts that reduce damage by 1/2 on a Failure. I struggled with this one, but a Crit Fail Save Shifts to a Failure and with this benefit further shifts to 1/2 damage which is like a Success and therefore a full Save Shift on top of the first one. Overall, there were so many Points and Shifts, the downgrade from 4 to 3 seemed to skew the classes a tad less while still representing how important Saves and Shifts are.
Factoring Primary Attack - I don't way to stray into "wildly complex," but consensus seems to be martials should get higher points for their primary attack, and so should casters. Therefore, I changed the Weapon Proficiency and Class/Spell DC to a 1, 3, 8, 14 progression from their previous 1, 3, 6, 10 for Weapons and 1, 3, 8, 12 for Class/Spell DC. This boosted fighter (now tied for first) and diminished Warpriest both as recommended. Rangers still keep up with fighters thanks to awesome saves, and Warpriests still have point advantages against cloistered thanks to saves as well but only by 1 point (I still think despite this, the chart highlights Warpriests don't compare well to martial or caster attack forms).
New Points (Average - 60.55):
Fighter - 77
Ranger - 77
Barbarian - 76
Monk - 76
Rogue - 73.5
Champion - 70
Bard - 60
Cleric, Warpriest - 49
Druid - 49
Cleric, Cloistered - 48
Sorcerer - 45
Wizard - 42.5
I have to keep reiterating the point: This analysis is not complete. It's not the end of the story on the classes. It's not intended to rank them. It facilitates comparison of core mechanics common to each class without straying into complex, subjective "wildly complex" mechanics.

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I added the APG classes:
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New Points (Average - 61.03):
Fighter - 77
Ranger - 77
Barbarian - 76
Monk - 76
Swashbuckler - 74
Investigator - 74
Rogue - 73.5
Champion - 70
Bard - 60
Oracle - 56.5
Cleric, Warpriest - 49
Druid - 49
Cleric, Cloistered - 48
Sorcerer - 45
Witch - 45
Wizard - 42.5
No surprises from Swashbuckler 74, Investigator 74, Oracle 56.5, and Witch 45