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New seed phrases are typically 12-24 randomly generated words, not user provided... and when you need to "change a password" in a crypto wallet, you can generate a new private key and move funds.
Check out BIP-39 [0] for more details.
[0] - https://github.com/bitcoin/bips/blob/master/bip-0039.mediawi...
Modern hardware wallets already implement hierarchical determinism, and have for a few years. Extending that further to do private keys per site wouldn't work on most chains I know due to chain state...
Details in BIP-32 [0] and BIP-44 [1].
[0] - https://github.com/bitcoin/bips/blob/master/bip-0032.mediawi...