To me, it seems anything but negligible, and seems like common sense.
The bigger block, the longer the time is required to process
it, and the greater the the risk of orphaning.
What am I missing here?
All the of expensive operations can be done before a block is found, then they do not add any proportional time.
Correct.
Miners
could agree to only solve blocks that the other miners are already expecting. This would mean that exactly
zero information about the block contents would need to be transmitted at the time of block-solution announcement. This would eliminate any block-size dependent propagation risk.