I agree that this is a system the game can likely do without… Professions mostly accomplishes it.
That said, I think the way to balance it would be to have a very short list of starting level equipment available. Basically, if it can be looted from a zombie maybe you can get it at the start for 1 point. I’m thinking toolbox, welder, wood axe, glock 19, a few things like that.
Still, while I can see how to balance it, I don’t really see why it is necessary