Exactly. Then merkle trees don't help you. They only work for static documents.
Merkle trees can work just fine for dynamic content. You just need to use a pubkey pointer.
1. https://beakerbrowser.com/2017/06/19/cryptographically-secur...
IPFS does this by storing (mutable link, contentID) pairs in the DHT, which can be updated if you know the private key for the mutable link.