The problem with using Windows auth for a web application is that many web applications store their application users' credentials in the same SQL database that is used for other application data.
So you have a chicken-and-egg problem. You can't authenticate the user before connecting to the database, and you can't connect to the database without authenticating the user.
It should be possible to use Windows authentication, and then also have application-specific attributes of the user stored inside the database. But most people find this cumbersome to administer, and also limiting to portability of the application.
For example, if one of the feature of the application allows users to change their own password, then the process running your web application needs the privilege to alter a Windows password, which may mean that the application needs to run with Administrator privileges.
If you let the application manage user ID for the context of the application, then to change a user's password is just an SQL operation, and your application is in charge of enforcing security for that.