There are two problems with passwords. Reuse, and site breaches. The solution to the former is the same as passkeys: credential managers. Passkeys genuinely solve the second, in exchange for a vastly less comprehensible system (see all the uncertainty people have even here on HN) that doesn't support many of the ways people want to use authentication tokens.
That's not what phishing is. Phishing is convincing someone to give you a credential with a page that looks like the one they're supposed to give the credential on. Passkeys cannot be phished.
No, the biggest issue with passwords is phishing. You can't phish a passkey.