The title is misleading. Merkle Trees are not used by every blockchain and they aren't always necessary.

The advantage of Merkle Tees in the context of blockchain is that they can be used to quickly and efficiently verify that any given transaction is valid in the sense that it exists within a specific ledger (as defined by the Merkle root hash of that ledger).

This feature is only useful for 'light clients' as it allows such clients to verify the validity of a transaction provided by a third-party node without having to trust that node and without needing to maintain a full copy of the ledger; the light client only needs to know the root hash of the blockchain in order to prove the validity of any transaction.

This feature is not particularly useful for Proof of Stake blockchains because you can achieve similar results by requiring a copy of the block within which a transaction was included and then you can verify that the transaction's ID was used to compute that block's hash.

You can then check the validity of the block by checking that it was signed by the expected block forgers/validators.

This approach for light clients covers the vast majority of use cases.