pathlib.Path() could wrap shutil.copy() with something like this:

def copy(self, target):
    if not self.is_file():
        # No support for directories here
        raise ValueError("Path must point to a regular file")
    # copy() appends filename when Path is copied to a directory
    # see shutil.copy() docstring and source for details
    target = shutil.copy(self, target)
    return self.__class__(target)

Docstring could be:

Copy file content and permission bits of this path to the target path
and return a new Path instance pointing to the target path.
If target is a directory, the base filename of this path is added to
the target and a new file corresponding to the target is created.
If target points to an existing file, that file is overwritten.

Since shutil.copy() accepts path-like object, I do not think there is a need to add the copy method to Path.

As for additional limitation, it looks arbitrary and application specific. You can easy implement a simple helper function as you just demonstrated. And you can easily modify it if your needs change (for example if you decide to not copy links). Not every three lines of code should be added as a function to the stdlib.

And just to add Serhiy's logic, think of pathlib more as an equivalent to os.path than a be-all solution to anything path-related.