They can, and hopefully will.
To get a new passkey on another device, the provider needs to allow you to prove you have possession of your other device first. They can do that by sending you a one-time code, for example, when you authenticate using your existing device, which you can then type in the new device, and that lets you associate your new device-generated key with your existing account.
With iCloud, you don't need event that because Apple can, and does, sync your keychain across all your Apple devices. So as long as you use the same Apple ID on different devices, all passkeys are automatically sync'd.
If you lose ALL your passkeys, you may be in trouble and for that reason, it's common that when you register your first passkey, you should also be given a long recovery code which you must keep privately in a very secure physical location (as that will allow anyone who can get it to reset your account). You could say that IS a password, and perhaps you're right, but there's a difference in my mind that's pretty big: you're never supposed to use that "password", nor keep it easily accessible or even anywhere in digital form.
Finally, a lot of people in this thread are missing that passkeys prevent phishing, and are basically the only way we know to prevent phishing. And phishing is extremely high in the ranking of security issues we currently have to try to solve.
If you know a better solution to phishing than passkeys, please let us know (Passwordd Managers are not that if they allow the clueless user to extract the password and manually enter it anywhere)!