That's not why governments don't (usually) make pencils though.

Not one person knows how to make a pencil, that's probably true, but there's no reason why one organization collectively couldn't have that knowledge, and I don't see how that would be different whether that organization is a public or a private sector one.

Within governments and pencil corporations it's the same exact people working there (humans), and from a manufacturing, engineering and logistics point of view how they operate could be identical. I say could, because there are a vast number of different ways to organize the supply chain for a pencil (or any commodity), regarding the level of outsourcing. You could just outsource everything from design to manufacturing to sales, or do one or all parts of that in-house. The reason why governments generally don't produce pencils, is the same reason why Apple and Pizza Hut don't. It's not their core business, and they see no benefit in investing in that area and bring in the expensive expertise required. For them it's much more economically viable to outsource it.