Reusing an address encourages a sender to go retrieve the address from a list of addresses somewhere that they are maintaining, significantly increasing the risk that they accidentally retreive the wrong address. If they retrieve the wrong address from their list, it will be a valid address and the wallet software won't stop them from sending to it.
It also encourages sloppy behavior. If you are copying and pasting a brand new address you have never used before, you are far more likely to double check it properly than you are if you are copying an address you've used dozens of times before. "This address has always worked fine before, so I don't need to bother double checking it this time." And then clipboard malware means you send the coins to an attacker.
There are some coins I don't want to be mixed together at all, that is why I have labels for addresses and transactions to make categorization in my wallet, similar like I would do with old style cash wallets.
I prefer using separate wallets entirely to prevent the risk of accidental combination of UTXOs I want to keep separate. Easily done by just incrementing the account number in the derivation path or using multiple different passphrases, meaning you don't have to go through the process of generating and backing up a new seed phrase each time.
To be more precise: owners need to protect private keys and chain codes (and indices in some cases) which are kind of a synonym for "extended private keys" (as in BIP-32). Do these terms fit better?
The terms are more precise, yes, but the advice is still misleading I think. As I mentioned above, I don't think 99% of users should ever be handling raw private keys, as it is completely unnecessary for them to do so and it just opens them up to additional risk. Even fewer users should be handling their chain codes for any reason.
Just back up and protect your seed phrase and be done with it. Everything you ever need (private keys, chain codes, extended keys, etc.) can be derived from that seed phrase.
