1. Proficiency Scaling.
This is debatably two related problems, the first (the one I think is an error) is that Sorcerers do not get to Expert with Unarmed (despite some Bloodlines giving Focus Spells entirely based on unarmed attacks) when they do with Simple Weapons, and Warpriests likewise do not get to Expert in Martial Weapons (despite getting Proficiency in them). These seem like errors because they are the only two times when a Class provides a weapon and encourages the character to use it then pulls the rug out from under them by not increasing Proficiency. That's a trap option, and bad game design policy.
Speaking of which, the second issue appears intentional, but remains a huge problem. Probably the biggest one in the game. You can get Proficiency with Armor or Weapons as a General Feat, but can never increase it that way. Now, deciding that General Feats should not allow you to cross class boundaries by getting good with, say, a Greatsword or Full Plate as a Wizard would seem reasonable to me on its own. The problem is that in that case, the Feats shouldn't exist in the first place. By existing, they allow the Wizard to do precisely that with General Feats,...
I would keep in mind that Wizards only ever get Expert with Unarmored Defense, and Expert with Wizard weapons. If you think of them in PF1, where they had only poor base attack, and only feat heavy, or spell power reducing options otherwise, this is still better. I for one, have always championed the idea that if your Wizard wants to wield a sword like Gandalf, he should be able to with some effort, but without strangling himself. However, that has never been an option in these games, so why should they suddenly be competitive with Fighter?
Also, the "Warpriest" is really the base Cleric from PF1 and all previous editions. Remember those guys with Medium base attack, and simple weapons.
After all, Gandalf was pretty handy with his bastard sword, but was he as good as Aragorn or Boromir? No, and we wouldn't want him to be.