A password manager on the other hand is just a place to store credentials. Credentials is a concept that most people understand. A password manager in this context could be as simple as a text file on your desktop (not a great idea), or the one included with your browser (a little better, but make sure you set a master password), but if you want more features there are more sophisticated options available.
Coupling authentication with encryption has its place, but I would think that it would work better when accessing a service through an app rather than a browser since the app publisher can create unique a key pair and sign the certificate with their own CA and use that for authentication, but in the context of a web app accessed through the browser copy-and-paste beats having to configure your client certificate per domain at least from a "user friction" point of view.