If you don't want your identity to be tied to one specific device, then you need somewhere to store your keystore that isn't on that device.
Technically you don't need a third or even a first party for that; you could self-host. In practice though, the overwhelming majority of users will be using some sort of cloud storage service. A third party service in this case is likely better than first party since I don't want to lose my credentials if I decide to use a different OS or browser, and browser/OS vendors haven't been great on cross-platform compatibility for credential storage thus far.
Technically you don't need a third or even a first party for that; you could self-host. In practice though, the overwhelming majority of users will be using some sort of cloud storage service. A third party service in this case is likely better than first party since I don't want to lose my credentials if I decide to use a different OS or browser, and browser/OS vendors haven't been great on cross-platform compatibility for credential storage thus far.