Basing the argument on information theory is problematic because there are 2 phases to the communication (txn exchange and block solution broadcast) and we are just focused on the second phase. Observations like communication must be proportional to # txns apply to the whole communication not its parts.
The fact that there are two phases in the communication is what allows the block solution to be compressed by a factor of γ (the coding gain). The model takes this into account.
