Usually "logging" is semantically relevant, and it better reflect on the return type. But well, it's pretty useless to log the execution of pure code anyway.
I agree that GP seems to be talking about print-debugging (one doesn't go changing his mind about semantically relevant logging), so everything on your comment is on the spot, but generalizing this can lead to confusion.
If you need to do "semantically relevant" logging from a pure function, just create a pure function to process the semantic relevant part to something generic (like a Text), and call the simple unsafe logging function on the generic result.
One is replaying critical failed requests when a downstream was offline and the other is gathering tracking statistics from apache access logs.
Everything else I would classify as diagnostic, wondering if you would consider that semantic as well.
Every kind of software has some error log, long lived servers tend to have some usage log too, databases tend to have journaling logs, and distributed computing tends to have a retry log. There are other kinds of them, like all those lines a compiler outputs when it tries to work on a program, or the ones a hardware programmer shows while working. Every one of those are there for the user.