And I also store them separately. But don't you agree that storing them in 1Password is still better than nothing, as there are still some use cases that you are protected against that way?
No, that's where you lose me. If you're using 1Password to generate passwords in the first place, then I really don't see how using it for TOTP accomplishes anything. To me, it looks like you could literally concatenate the TOTP secret to the 1Pw-generated password and have the same level of security.
In particular OTP codes are intended to be single use they're a ratchet. If a site does this properly then any OTP code you steal from me is not only worthless when it naturally expires, it's also worthless once I use that code or a subsequent code to authenticate. If you used a passive keylogger that may mean by the time you get the key events that OTP is already useless. Likewise for shoulder surfing attacks.
Note that a prover may send the same OTP inside a given time-step window multiple times to a verifier. The verifier MUST NOT accept the second attempt of the OTP after the successful validation has been issued for the first OTP, which ensures one-time only use of an OTP.
The question is whether there is any point in having an OTP secret if it's stored in the same location as the password.
We're not talking about stealing single codes, but the entire secret.
With HOTP the answer is yes, because of ratcheting. A clone of the secret doesn't let you impersonate the original device, because their counters will conflict as both are used.
With TOTP the answer is no. You can make codes freely, and the clone is indistinguishable from the original.
The rule you cite is basically irrelevant. It just means that original and clone can't log in at the exact same time.
You've short-circuited by assuming the threat model is a bad guy breaks into 1Password. But there's no reason to insist upon this very unlikely threat model, there are other threats that _really happen_ in which having both OTP and a password under 1Password saves you.
Getting obsessed with a single unlikely threat leads to doing things that are actively counter-productive, because in your single threat model they didn't make any difference and you forgot that real bad guys aren't obliged to attack where you've put most effort into defence.