Could someone explain to me how the nodes should select the heaviest subtree, when they don't have that information? It requires information from all(!) other nodes. How can this even make sense, because one node is connected to say 8 peers and not the entire network?
Block headers could be broadcast for orphaned blocks. However, it is possible that 2 nodes will have different headers accumulated.
With a linear blockchain, proof of work is always exactly agreed by all miners.
Since all block headers are linked. All nodes can agree on the proof of work linked to a particular header. If a node was missing any blocks on that chain, then it wouldn't be able to form the chain at all.
With GHOST, 2 nodes could disagree about the proof of work for a particular chain. There is no way to be sure that you have all the orphans.
In practice, this isn't really a problem, because the 2 rules almost always give the same answer.
If you did push the the block rate to a point where network latency is a problem, you could have 2 chains where there is disagreement.
Ensuring that all headers are well distributed between nodes is critical. Disagreements are not likely to last long anyway.