Working for a company that takes copyrights very seriously, we are required to put copyright/licence messages in every single file, despite the fact it’s not technically required under US law.
I suspect it’s so that, if a file was somehow separated from the product as a whole, it would still be easily identifiable.
However, we don’t maintain that message in every single file. We have scripts which automatically add in the copyright messages to every file that’s released to the wild. That way you only have to change one file.
We also have scripts that check every single release file has the correct message.
However, in terms of licensing, the lack of an explicit licence means that standard copyright would apply so it may be that you’re happy with the single LICENCE.txt file.
As always, my legal opinion is worth every cent you paid me for it (which is zero). I am not a lawyer, I am certainly not your lawyer.