This is not correct. When I set up TOTP 2FA, the site generates a seed and tells it to me. It is always valid and always reusable, and it's no more difficult for me to communicate it to anyone else than it was for the site to communicate it to me.
Think of the physical one-time tokens: If I know the data stored on it, I can replicate them too. So, are they "something you have", or "something you know"? The reason why they're "something you have" is that it's easier to have the physical ownership of the device, than to know they "secret" of the device. But, the same is true about Google Authenticator! In that respect, Google Authenticator can be, indeed, interpreted as "something you have".
If you're building a consumer service, that's a big improvement over someone picking their dog's name and saving it in a Word doc on their desktop.
1. Passwords are selected by the user; you cannot prevent reuse. While it's technically possible that a site could allow you to set the TOTP seed nobody does.
2. Password entropy is notoriously hard to calculate programmatically – e.g. well known movie passwords or leet-speak are often judged as stronger than shorter true-random sequences – but you generate the TOTP seed.
4. As with #1, preventing reuse is hard. Knowing that all extent implementations offer fairly strong protections against accidents is a key difference.
Your finally point depends on how you judge the whole system: “something you know" can be told to someone else, which isn't true of TOTP. It's also always valid and reusable whereas the one-time code is closer to an on-demand verification. From the perspective of security boundaries, a desktop user accessing a separate token, phone, or arguably even an iOS user using a separate app is closer to something you have than something you know.
TOTP isn't the strongest form of MFA but it's closer to that end of the spectrum and, especially in consumer contexts, a huge improvement over nothing. In the real world, those kinds of security improvements are still meaningful even if they're not perfect implementations of a textbook concept.