Why storing users passwords at all?
Because for many applications, they don't want individual user accounts connecting to the database. The users/passwords/rights/permissions is all handled at the application layer, and a single dedicated service account is used to connect to the database back-end.

As a DBA, I don't want to have to manage, at the database level, the 10,000 active users of some medium-sized public-facing web application, or maybe the 2+ million users of some suddenly popular app.

In a very real sense, this is a difference in philosophy between application developers and database developers/DBAs.

Many/most application developers are not going to want to pass responsibility for major aspects of app functionality and/or business rules down to the database layer. Instead, they view the database as a tool to simply store and retrieve data.

In some cases, this might be short-sighted; many RDBMSes do have awesome features that could make app dev lives much easier (row-level security, columnar indexes, filestream storage, etc.).

But some of these cooler features are only available in newer versions, and organizations aren't always quick to upgrade existing environments (see this chart from 2014). 

And in other cases, handling those things at the application layer is preferred (and not just for database platform portability, I frankly think that claim is overblown).