Are we talking theoretically, or in practice? Because I don't think sharding will ever be implemented in Bitcoin. It completely trades off redundancy -- the backbone of the P2P protocol -- for scale. Ethereum is being forced to consider it because of its unsustainable throughput demands, but the "decentralist" camp won't let it happen in Bitcoin.

Maybe we should start by identifying the exact issue. How do you define this "Bitcoin scalability problem?"