* They effectively entrust the keys to your entire digital life to (right now) either Google or Apple. Account compromise, or a ToS-related suspension, becomes catastrophic.
* Domain changes happen (acquisitions, rebrands, etc.), and there is no way to share or migrate passkeys between domains. Right now the best you can do is a highly manual process involving the user authenticating on the old domain, registering a new credential on the new domain, and somehow linking them. This process itself could be highly vulnerable to interception, since every site would likely have to build a bespoke way of doing it.
* There's no way to migrate your passkeys between ecosystems. So if you're an iPhone user, and all your logins are iCloud Passkeys, it becomes really hard to switch to Android.
* Password-sharing is regrettably used a lot right now, but it's the simplest thing that works. For example, I and my husband have a shared 1Password vault for things like utility and streaming account logins. Right now none of the Passkey syncing providers support anything like that (and I feel like they won't, because it'd be a huge vector for scams).
I think the password is going to stick around until these issues are addressed.