This was not a strawman. I have not mis-represented your argument.
If you have a block and wait instead of broadcasting, someone else could broadcast their block in that time, which would mean the network would start mining on their block instead of yours and you would be left with a stale block instead of 25btc rewards.
very clearly suggests that the first to broadcast will receive the attention of the network as a whole, guaranteeing that a later broadcast rival block will become an orphan.
You've merely changed your argument to:
If you broadcast sooner, it is more likely that more of the network will recognize your block over another.
Unfortunately, while true, this is insufficient to support your earlier claim:
Unless a pool has over 50% of the mining power it will always be bad for them to delay a broadcast...
You misrepresented my argument saying I thought the propagation was instantaneous. I didn't suggest the first to broadcast that the network would immediately recognize theirs, I only implied that it could be propagated in that time "someone else could broadcast their block in that time".
Certainly, a pool wants to reduce the probability of its blocks becoming orphans. To this end, the broadcast strategy: "broadcast as soon as possible" is optimal. However, a pool will also want to reduce difficulty so that it is able to find more blocks. To this end, the broadcast strategy: "broadcast a block only once a rival block has been seen" is (roughly) optimal. It is not clear that the first concern always outweighs the second (for pools controlling no more than 50% of the network by hashrate), especially in light of the fact that some nodes are better connected than others.
If you broadcast block-you-found 1 and that is chosen as the winning block by the network, then you have 1 block. If you keep mining on that block, you will keep having the same chance of having your block winning. If you wait until you have 10, you will only win if 10 haven't been mined in that time. You aren't giving anyone an advantage by letting them mine on your blocks because it's either your blocks or someone elses blocks they're going to be mining on.
Question: What does this obscure example of a network with terrible rules have to do with anything?