Immutability means you can’t change history not that you can’t update state. If my utility company needs my new home address and they use a blockchain for some reason (maybe part of a near-realtime electricity payment system), I can always sign a transaction to associate my blockchain address with my new home address. Perhaps the electricity equipment itself can sign my signature to ensure that I am physically located with it and have authority to change who it’s representing.
But what happens if you lost your keys and no central authority has the ability to change your address?
Maybe if it is a physical address. After all, you presumably live there. But what if it's just some payment contract? As far as they care you yourself signed it, and they have the proof. If you can get them to cancel the contract, what was the point of using blockchain anyway?
But the whole point of Bitcoin is that no one should have the authority to reverse transactions or print new coins. And all of Web3/Eth/NFT crypto shares the idea that this technology is useful because it removes the need for trusting a central authority (you trust the code and the distributed network instead)
The idea is that you have the coins and NFTs in your own wallet and no one can take those away from you. So if you are going to add a layer that allows transactions to be immutable you are literally describing a bank or a credit card and there is no need for crypto.