But which is more important for broadcasting to the world, outbound? Is the only advantage of inbound to run a node for others to sync their blockchain databases?
You need at least some inbounds open so that you can detect if somebody already solved the block you're trying to find so that you don't waste precious milliseconds on it. You don't need a lot of them, and as kano said, connections (inbound as well as outbound) to all the major pools is enough.