What are the best practices for managing empty, unwanted wallets?

First off, you should consider if you actually need to abandon your current seed phrase. Reasons for that include:

1. Your seed phrase has been compromised. In this case you need to move your funds to a safe wallet as quickly as you can before someone steals them.
2. Your master public key has been leaked. This means any past and future transactions done using this seed phrase will not be private anymore. (Wallets using hardened derivation do not permit a master public key, some permit account-level extended public keys which only generate addresses for a single account. If an extended public key leaks then you can usually just stop using that one account.)
3. You are moving to a higher-security solution (e.g. from a software wallet to an air-gapped hardware wallet) and thus need to also replace your seed phrase that was previously generated in a less secure environment.
4. You are moving to a wallet or backup system that is incompatible with the previous seed phrase (e.g. from a single BIP39 seed phrase to a 2-of-3 Shamir backup).
5. You've sold all your bitcoin and have no plans of coming back.

If you've determined that you will not be using this seed phrase going forward, then I would argue you should either keep the seed phrase or keep nothing at all. Keeping just the master public key will not protect you from any dangers compared to keeping the seed phrase, as the knowledge of either is now (with the wallet empty) merely a privacy leak and does not conclusively prove ownership. And as you've mentioned, keeping just the public key increases risk of accidentally burning funds.

So here are some reasons that come to mind to keep the seed phrase:

1. One or more of the associated addresses is or was at some point publicly available (like a public donation address). Even if it has been taken down, it's still possible that someone has saved it or reposted it elsewhere and in case it receives some coins you will want to be able to spend them.
2. You want to keep a backup of all transactions that have happened in the wallet. Again, this is mostly just for you, as a seed phrase does not conclusively prove ownership (especially for an empty wallet).
3. There are local laws and regulations that might at some point require you to submit a non-conclusive proof of ownership for that wallet. (Some countries currently require such "proofs" for withdrawal addresses.)

Personally I would hold on to any retired seed phrase unless it was only used to play around with a few sats. The storage requirements for a seed phrase of an empty wallet are much lower than for an actively used wallet, and you are probably safe keeping them all in one place, so it shouldn't take much effort.

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