Lnbits auto generates wallet ids (random hex) which via the logs could be traced to the scan ranges on the Oracle side. It needs it so that it can display UTXOs on the client side. Importantly spend private key stays on the device, so noone else can spend it. For a full total privacy, the solution can be hosted on your own infra, if in doubt what happens to that metadata.
Very much doubt that CEXs will ever implement them, as they need to stay compliant in a jurisdiction in which they operate and SPs make life much harder for on-chain surveillance companies they have to work with.
you wouldn't want to store large amounts anyway.. just so you can make/receive payments with privacy in mind.. 12 word seeds are not stored anywhere.. scan and spend secret keys are encrypted and if your session is compromised so can be the keys... not easy either for the attacker..
Thrilled to announce Thrilla - #SilentPayments#Bitcoin wallet harnessing the power od #LnBits and #BlindBit indexer. Self-custodial as keys stored in local storage on the browser. Check it out at: https://thrilla.me