Of course if someone is memorizing the TOTP seed and generating the proof on the fly every time, then there's no shift in factor, but no one is doing that. And if they're saving the password on the same device that stores the TOTP code, then we're back to one factor, but now it's just 2x "something you have" at that point.
An attacker. Your knowledge is much less interesting that the knowledge the server has, which is what the attacker can obtain. Grabbing a TOTP key out of a database is not materially different than a password.
TOTP's different characteristics mean it's harder to intercept, but passwords tend to be stolen nowadays moreso than intercepted, if only because you can intercept only one at a time but can steal the entire database.
The different characteristics mean it can add a bit of utility to a normal password, but I think it's less night-and-day than it was presented as.
All the things around improving web authentication are just about people not having to memorize that something you know and protecting it against eavesdroppers.
That's reductionist way past the point of being a useful model of authentication factors.
By that logic, even biometric factors are "something you know", as you can always (with a lot of effort) physically replicate a fingerprint/retina/genome you have a sufficiently high fidelity recording of.
You clearly mean that as a reduction to absurdity, but, yes, I mean exactly that. Pretty much said so.
It is "reductionist" if you insist the only valid framework is "what have have/know/are", and you view what I'm saying as the intersection of what I'm actually saying and that model. I am claiming the have/know/are is reductionist, and to a large degree outright wrong, because it is focusing on the wrong thing. Look at it the way I'm looking at it and the authentication questions become richer and easier to understand.
Unfortunately, it also means that there's more things that are either hard or impossible than the have/know/are methodology promises, because two of the things that methodology promises effectively don't exist. (Unless you are controlling physical access, and willing to spend a lot of money on hardware and human verification of the correct use of the hardware.) But since I believe that is an accurate reflection of reality, blame reality, not the model.
While the "something you x" model has many limitations (and I practically disagree with some regulatory bodies on what does and does not constitute a "true" expression of one of these factors), I don't think that these limitations refute it in the abstract.
TOTP was what really kicked me into thinking this way. They tried to make it "something you have". They tried to lock it behind apps and pretended really hard that it wasn't just a particular shared secret... but it is. It's just something you know.
The rule is, if it could be stuck in your password manager, it's a thing you know. That includes even things like Yubikeys, which are things that can be cloned and stuck in a password manager. They're just really, really hard to clone, and that's a valid step up from "a password". I'm not saying that the differences between all these "things you know" are irrelevant; they matter a lot. Having a password + a TOTP is a legitimate step up from having just either one alone. I'm just saying that analyzing things in terms of the other two factors isn't particularly relevant.