I think you are confusing the responsibilities here. The "login screen" is not Apache's doing. The process goes like this:

1. Browser requests page
2. Server says "this is part of area XYZ and is password protected"
3. Browser asks user: What's the password for area XYZ please?
4. User types password
5. Browser remembers password and area and uses it whenever server says "this is area XYZ"

In other words, even though you don't get asked the password anymore once you've typed it, this is not because the server has "authenticated" you. It is because your browser is sending the password along with every single request.

So if you want users not to see the password dialog, you have to tell their browser the password, and thus the user can still find out what it is.

Makeshifts last the longest.