A password manager relies on a single point of failure secret (master password), while the website-hash approach relies on a single point of failure secret (master key derivation algorithm).
It's really no different, so I think there must be some human biased thinking at play. Except the password manager requires a central or synchronizing computer system, while the in-head key derivation approach requires no such thing.
The trade off is that pass mgnrs give more convenience, but have slightly more failure modes (not knowing the master password, not having access to the synchronization or master vault, not wanting to log into a pass mngr on a potentially compromised computer when you only need a single password you are willing to sacrifice) while the in-head approach has a single one: not remembering the derivation method.
ETA: both are sensitive to sites changing names or URLs. But password managers more so (requiring extra searching and clicks) while in a mental key derivation context, you would probably remember "oh, it's protonmail." without explicitly needing to distinguish "login.proton.me" from their old URL. But, that does make the key derivation approach slightly more susceptible to phishing. Not seeing the password autofill at least gives mental pause.