I don't think that assumption is true because it should be far more easier to brute force the master password of a deterministic password manager. Worse, the OP's solution accepts "password" as a master password, which means that many, many people are going to have the same generated passwords if this gets widely adopted.

That's... not reassuring. Though I would still argue that that is more of an implementation issue, not a deal-breaker for the general idea. And there are many KDF variants that (claim to) offer protection against brute force, so that's not necessarily an issue either (but I do agree it sounds risky).