The only difference between "" and <> is that the former adds the current file's directory to the beginning of the search path.
So the only reason to use "" instead of <> is when you need that behaviour, because the dependency is relative to the current file.
If you use "" in any other situation, then you are introducing a potential error, because now someone can change the meaning of your code simply by creating a file with a name and location that happens to match your dependency.
(Yes, some compilers have -isystem and -iquote which modify that behaviour, but those options are not standard, and can't be relied upon. I'd strongly advise against their use.)
So the only reason to use "" instead of <> is when you need that behaviour, because the dependency is relative to the current file.
If you use "" in any other situation, then you are introducing a potential error, because now someone can change the meaning of your code simply by creating a file with a name and location that happens to match your dependency.
(Yes, some compilers have -isystem and -iquote which modify that behaviour, but those options are not standard, and can't be relied upon. I'd strongly advise against their use.)