What is the worst an attacker could do with full control over the blockchain?

What is the worst an attacker could do with full control over the blockchain?

Let's assume somebody gains control over 100% of the hashing power and is now free to mine and control as many new blocks as he wants. What would happen?

The attacker still could not include any fake transactions into his blocks, because other nodes could easily detect that the transaction wasn't signed by the wallet owner.

The attacker could include some double spends from his own wallets, but again, this could easily be detected.

So, the other nodes would simply ignore his blocks as invalid. Maybe they would crash and require a fork, or they would recover and wait for the next valid block to be mined and broadcast.

It seems to me that there isn't really anything to gain from controlling the hashing power. Am I msising something?

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