In this case, there is nothing more anonymous about the Ethereum approach than a simple username/password. But there are some benefits in terms of data privacy. Most websites, especially social media, don't let you get away with just an anonymous username/password these days if you want to use their full functionality. They may want all kinds of other information from you, e.g. email address (3rd party), your phone number, ID verifcation, linked Google account with certain permissions to access private data, and so on. This data will be sent to their servers (as well as ad providers / Google) and linked with your identity. You have little control over this and can't remove it from their servers either.

With the Ethereum approach, you can control this data about yourself. For example, with zero-knowledge proofs you could prove to a service that "I am over 18 and an US resident with a valid phone number" without sending any actual information about yourself to that party. Twitter shouldn't need your phone number. It just needs to know that you have one.

Logging in with your Google account everywhere is convenient because it contains all kinds of facts about you. But you have no control over what's done with that data, either by Google or the service you're logging into. With "Log in wit Ethereum" you could get the same conveniences, but you still own your data and have full control over what's being done with it or who can access which parts of it.