A few additional points for Craft or Profession skills probalby won't break anything. However, you do have to be a little careful with Knowledge skills. Only Bards and Wizards have all knowledges as in-class skills. Suddenly allowing everybody access to these then intrudes on a strength of these classes.
In general, though, I kind of like the idea that the lifestyle of most PCs simply doesn't leave room for much else. Being a Fighter is as much a career as being a weaponsmith. So, the Fighter shouldn't generally be able to be a terribly good weaponsmith, just as the weaponsmith cannot be a terribly good fighter.
There's also a benefit to not giving too many such skill points to PCs - it keeps them interacting with NPCs. If they don't have a skill, they can go out and find someone who does. The more interaction you get with NPCs, the more opportunities you have for plot.
Let us also remember that one can "round out" a character without actually spending skill points. The character can have an interest in cooking, and try to do lots of cooking, without having a specific skill.
In general, though, I kind of like the idea that the lifestyle of most PCs simply doesn't leave room for much else. Being a Fighter is as much a career as being a weaponsmith. So, the Fighter shouldn't generally be able to be a terribly good weaponsmith, just as the weaponsmith cannot be a terribly good fighter.
There's also a benefit to not giving too many such skill points to PCs - it keeps them interacting with NPCs. If they don't have a skill, they can go out and find someone who does. The more interaction you get with NPCs, the more opportunities you have for plot.

Let us also remember that one can "round out" a character without actually spending skill points. The character can have an interest in cooking, and try to do lots of cooking, without having a specific skill.