TYPO3 Core

Why do you want to remove it?
It is a useful function!
Does TYPO3 6.2 support only FAL now and no file links like before - even for extensions?

First: This has nothing to do with FAL.

This is part of a usability cleanup in the backend (of course just a tiny part of it). See:

https://projects.invisionapp.com/share/H2IU7YVE#/screens/10259995/comments/6169346

The functionality is very limited, unintuitive, misplaced (finding files in "DB Check"?) would need core maintenance, security considerations and usability improvements to be really useful in a professional product. Such a feature is very seldom needed and can be best addressed by a third party extension.

To answer your second question: No problem if you want to access your files directly (without FAL) from your extensions, you just don't get the benefits of FAL.

If you access files throught the backend, core content elements or via TypoScript, you are already using FAL.

Sorry. You are right.
I confused it with the raw search in DB check that gives you the possibility to search the database using a filename and find the record(s) referencing it.