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+1 I agree with not requiring a feat to learn a new weapon.
Maybe a new weapon category though. But that makes sense to keep it within classes. If you want to pick up those weapons, take a level in that class or somehow multiclass in it. I disagree vehemently with requiring a whole feat for just one weapon.
I'd like to see all dwarves know how to use all axes and hammers, all elves to know how to swing a shortsword or longsword and a bow. Even better, add that as a background. If your background can tweak the skills you gain access to, why not the weapons?
I don't see why only an elf wizard can use a longsword, but a human one with the right background can't. Gandalf, anyone? well, he was a demigod, but the point remains. If you pick a weapon-focused background you should be able to mix n match. Wizards focused on their spells should be more likely to pick a background that benefits their core competencies.
That said, I'd like to see people be able to pick up single a free weapon prof or a skill prof at level 5, without spending precious feats.