@chriswilmer: Yes, that's correct. Sending twice the information takes twice as long, over a given channel. So the only way you can remove the propagation time's dependance on block size is if the amount of information sent when the proof of work is solved is constant (i.e., it doesn't depend on the number of transactions in the block). For example, you could send just the block header with the solved PoW along with a reference to the pre-propagated contents of the block.
With such a scheme, the miners need to pre-propagate the entire block contents (including the ordering) ahead of time and come to approximate consensus on that, prior to the proof of work being solved. But they can only come to (pre)-consensus on the block contents at the rate at which they can transmit information to each other, which places a limit on how quickly new transactions can be added to the "pre consensus." So even if you assume such a scheme exists and assume that miners follow it [1], the "supply curve" will turn upwards at some point for blocks that are larger than how much information can be transmitted between the hash power in 10 minutes.
[1] We know rational miners won't follow such a scheme because it means they cannot include recent transactions in their block candidates--even if those transactions pay a very high fee--because the miners haven't come to pre-consensus on those new transactions yet. In reality, rational miners will include these new transactions if the fee is greater than the expected loss due to the increased orphaning risk.
With such a scheme, the miners need to pre-propagate the entire block contents (including the ordering) ahead of time and come to approximate consensus on that, prior to the proof of work being solved. But they can only come to (pre)-consensus on the block contents at the rate at which they can transmit information to each other, which places a limit on how quickly new transactions can be added to the "pre consensus." So even if you assume such a scheme exists and assume that miners follow it [1], the "supply curve" will turn upwards at some point for blocks that are larger than how much information can be transmitted between the hash power in 10 minutes.
[1] We know rational miners won't follow such a scheme because it means they cannot include recent transactions in their block candidates--even if those transactions pay a very high fee--because the miners haven't come to pre-consensus on those new transactions yet. In reality, rational miners will include these new transactions if the fee is greater than the expected loss due to the increased orphaning risk.