So, there are several ideas about how to reduce the size of blocks being sent on the network:
* Matt Corallo's relay network, which internally works by remembering the last 5000 (i believe?) transactions sent by the peer, and allowing the peer to backreference those rather than retransmit them inside block data. This exists and works today.
* Gavin Andresen's IBLT based set reconciliation for blocks based on what a peer expects the new block to contain.
* Greg Maxwell's network block coding, which is based on erasure coding, and also supports sharding (everyone sends some block data to everyone, rather fetching from one peer).

However, the primary purpose is not to reduce bandwidth (though that is a nice side advantage). The purpose is reducing propagation delay. Larger propagation delays across the network (relative to the inter-block period) result in higher forking rates. If the forking rate gets very high, the network may fail to converge entirely, but even long before that point, the higher the forking rate is, the higher the advantage of larger (and better connected) pools over smaller ones. This is why, in my opinion, guaranteeing fast propagation is one of the most essential responsibility of full nodes to avoid centralization pressure.

Also, none of this would let us "get rid of the block size" at all. All transactions still have to be transferred and processed, and due to inherent latencies of communication across the globe, the higher the transaction rate is, the higher the number of transactions in blocks will be that peers have not yet heard about. You can institute a policy to not include too recent transactions in blocks, but again, this favors larger miners over smaller ones.

Also, if the end goal is propagation delay, just minimizing the amount of data transferred is not enough. You also need to make sure the communication mechanism does not add huge processing overheads or adds unnecessary roundtrips. In fact, this is the key difference between the 3 techniques listed above, and several people are working on refining and optimizing these mechanisms to make them practically usable.