The actual transaction data would still have to reach every node in the network.
Yes, but it should be in the mempool when verified close to the time of mining, shouldn't it ?
I think so.
Then it would have to be stored along with the blockchain (i.e., this doesn't help if the amount of persistent storage is an issue) and you'd need some mechanism to update nodes that don't have that data, plus you need to handle cases where, say, a new block overtakes a transaction referenced by it, but I think the "tip" of global activity should generally not need much extra work.
- Werner
But what I don't see is how using hashes is any better than simply increasing the block size. You can make use of the fact that most miners already have the transactions of the new block in their mempool even if you don't use hashes. And as far as I know that is already being done at the moment.