Files excluded but not ignored

I prefer to not add core.* files to my ignore listings because I find it helpful 
to see them in git status -- It helps me notice and clean them up periodically.  
Not having them ignored is also good ,because it allows git clean to care of 
core.*  files.

The problem is that git add -A, git stash -u, etc, remain interested in the core 
files.

Trying to start up discussion of whether there would be merit to a "half-
ignored" state -- Files which are excluded from tracking, but which still 
show in git status, and which are removed by git clean.

Not trying to propose yet how .git/exclude or .gitignore would be formatted 
or anything like that.  Just looking for opinions on whether such a state 
would be considered by the community as a good thing and merit the added 
complexity in the code.