You're logging in so they know who you are, but you refuse to keep a cookie in your browser so they won't know who you are?
You know what the problem is, you just refuse to fix it.
You know what the problem is, you just refuse to fix it.
It is odd you are pathologizing what I would expect to be normal behavior. It's not common behavior, but it doesn't seem abnormal for user agents to do this.
Edit: for users who only access their Google accounts via shared machines like at a public library, not having a persistent cookie on every auth attempt is going to be the expected scenario.
For someone who is tech-savvy and owns a laptop, there is a simple solution: create a new, vanilla browser profile and use it only for logging into Google. (I do the same thing, but for Facebook.) You'd don't need any privacy extensions when you want them to know who you are.
It also presents an attack vector to screw up everyone's logins and repeatedly force users to re-2FA every few minutes.
I also don't quite understand your threat model here and the details of what you're proposing is an attack. If you are a user who Google consistently knows has a persistent cookie at auth time, Google can expect that in the future and therefore use that as a data point in risk based authentication. If you are a user who Google consistently knows doesn't have a persistent cookie at auth time, Google can't rely on that data point providing any signal in risk based auth, and seems to be DoSing, or at least frustrating, users in that scenario.
I can't quite respond to your comment because I don't fully understand it.
The two sentences are not in contradiction at all. As long as he has the credential (password and perhaps 2FA), he should be able to log in. The cookie is a convenience, and should not be a requirement.