It really should be in all files, not because it’s legally necessary, but because it’s the best way to ensure that the correct license/copyright follows the code to which it applies.
Consider future contributions; the contributor’s copyright should apply only to the files to which they contributed.
Similarly, consider any code that you incorporate from external sources; that code’s copyright and license should only apply to the files in which it has been incorporated.
Lastly, consider the case where the code is copied out of your project to be incorporated in a different project. The license and copyright should follow with those files (and if your files don’t include copyright and license at the top, it’s very likely the person doing that copying will insert it themselves for this same reason).
Sufficient but a good idea to put copyright in all files.
Technically if there's no license found then it should be considered automatically copyrighted, with no permissions to copy. So leaving copyright license out actually makes it less open source.
I said it is not legally necessary to have that in every file in the previous comment solely to contradict the idea that his project level LICENSE file did not constitute a license for the individual files. I did not at any time suggest that it was not a good idea to put notices in every file. In fact, if you look at my other comments, you will see that I said that he should have put copyright notices into every file multiple times. I even said it at the root of this thread:
Consider future contributions; the contributor’s copyright should apply only to the files to which they contributed.
Similarly, consider any code that you incorporate from external sources; that code’s copyright and license should only apply to the files in which it has been incorporated.
Lastly, consider the case where the code is copied out of your project to be incorporated in a different project. The license and copyright should follow with those files (and if your files don’t include copyright and license at the top, it’s very likely the person doing that copying will insert it themselves for this same reason).