Is there a relationship between hashrate and bandwidth? If by increasing blocksize and thereby increasing bandwidth, would that eat into the available bandwidth for hashing? For example, if a peta-miner maxes out their bandwidth with just hashrate, then increasing blocksize would lower their hashrate. They would have to buy more bandwidth if it is available. It might favor miners living where there is better internet connectivity rather than cheap electricity or cold climate. It could help decentralize mining by enlarging the blocksize.
There is a subtle, but important relationship between hash power and bandwidth. The hash power / bandwidth relationship can best be looked at in terms of orphan blocks. A miner needs to have adequate bandwidth to make orphan blocks unlikely. What is adequate? What is unlikely? Assuming 10-minute blocks, each and every second there is 0.16 % chance a miner will discover a block. If you're a miner, and you find a block, you obviously need to broadcast it to the network ASAP. A 6-second delay in publishing would mean 1% chance that someone else finds a block in the meantime. Diminishing returns help to keep the bandwidth 'race' to a minimum. Having enough bandwidth to keep your orphan rate under 1% would probably be good enough. If your mining operation was big enough that 1% was a substantial sum, perhaps you would buy bandwidth to push the orphan rate down to 0.1%, but at some point it no longer makes financial sense to invest in more bandwidth. Consider that being able to push out blocks infinitely fast would mean paying for infinite bandwidth, but at best would mean 1% increase in returns over the miner who took 6-seconds to publish a block. Also, as miners are not required to include any transactions in blocks they publish, they have another way to compensate for low bandwidth bottlenecks - publish empty blocks (this is because - currently - the block reward is so much bigger than transaction fees are). Since orphan blocks divert hash power away from the main chain, they are a security consideration, and if the system design encourages miners to publish empty blocks, that certainly doesn't help the network to thrive either.
The block-propagation-race issue could certainly be impacted by larger block sizes. Fortunately a protocol is being (has been?) implemented that allows blocks to essentially be per-constructed in real time, by each miner, as transactions flow across the network. If that system was perfectly successful, the miner who finds a new block would just need to transmit the block header, and the block header does not scale with transaction volume. Another way of thinking about it is this: Currently blocks are pushed out all at once, creating massive peak loads on miner bandwidth. The new design spreads out the load over the whole 10 minutes between blocks (or however long).
Miners would always need to have enough bandwidth to comfortably process the entire transaction load on the network. I currently have a 20 Mbps down / 5 Mbps up cable connection here in Washington State, USA. It cost me $45 per month. That is 1,500 MB down and 375 MB up every 10 minutes. That equates to 10,000 TPS down and 2500 TPS up, respectively.