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Some coins do sharding by not using a blockchain at all. e.g. RaiBlocks [1] uses a "block-lattice" approach. It is a Proof-of-stake-secured coin.

Sharding isn't any easier with the Tangle.

Proof of stake is not trustless.

Indeed, that's the case. It's an important distinction, but one which may not matter as much as it used to.