Blockchain (or more correctly "hashchain"[1] data structure) doesn't solve the double spend problem, because anyone can create a new entry with a hashpointer pointing to the last entry (aka "block") with transactions.

This problem is inherent in all Nakamoto Consensus style implementations (basically Leader Election algorithms), not just Bitcoin's PoW.

Simpler: anyone can fork the blockchain and over-write the ledger with the new transactions. So in reality the double spend solved by the social consensus on the right fork, not by technological solutions.

EDIT: Leaving aside the question of transaction finality and probabilistic nature of the Nakamoto Consensus, which making it even worse.

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[1] https://en.wikipedia.org/wiki/Hash_chain