I want my cross-cutting concerns to be as invisible as possible, I definitely do not want them to proliferate through all function calls I make in the app.
I do not believe domains or async hooks is too much magic, and they are pretty sound when used properly. As long as they are used responsibly and in a limited setting it is just the right amount of magic.
Logging should not happen inside libraries or submodules. Libraries should expose errors and exceptions either via throwing or message passing (e.g. dispatching error events). Logging should happen at the top-level of the application from a central place (logging logic should not be scattered all over the source code). The top level application logic should aggregate errors from children components/libraries and decide how to log them. This makes it easy to change the default logger and to customize various aspects of the logging.
When you scatter logging logic everywhere throughout your source code, you break the principle of separation of concerns which is probably the most important principle of software development. Even the term 'cross-cutting concern' implies a violation of separation of concerns (a violation of the cross-cutting kind to be exact). A concern cannot be both separate and cross-cutting.
That's because logging is not a concern of your app -- it's a secondary need that's orthogonal (hence cross-cutting) to its actual concerns, and which is there regardless of the app.
Changing your whole app's structure just so that you collect things to log in a central place (as you propose), would be the real violation of concerns.
Not to mention this way you pass around information that might be useless for the purposes of the app (and is just needed for debugging), that it's enough that separate components know themselves internally.
Maybe it depends on what kind of language/platform you use but if each component is able to dispatch events on itself instead of logging, then that does not require changing the whole app's structure.
The only concern of the top level application logic would be monitoring/reporting so logging fits naturally under that label.