Bear in mind that nodes already tell each other about what transactions they have and their peers track that, via inv broadcasts and mapAlreadyHave.
If you have already sent a "template", then you can confirm a block by sending the 80 byte header and a 32 byte hash.
To distribute a block with 2000 350 byte transactions requires
Full Block: 2000 * 350 + 80 = 500kB
Header + tx hashes: 2000 * 32 + 80 = 64kB + coinbase
Header + short hashes: 2000 * 4 + 80 = 8kB + coinbase
Template: 32 + 80 = 112 bytes + coinbase
If the coinbase was included in the template, then it is simply 112 bytes.
If the template is sent 16 times per block, this represents 16 * 32 * 2000 = 1MB of extra data. This means a 3X increase in network traffic.
If templates required 1/4 of the block difficulty, then sending the templates would require 50% increase in network bandwidth.
However, there is nothing preventing someone from reusing a template. A miner who receives a template could verify it, and then just mine against it.