Regarding iTunes, one detail about Carbon that is sometimes forgotten is Carbon originally ran on Mac OS 8 and 9 to facilitate the transition to Mac OS X (https://en.wikipedia.org/wiki/Carbon_(API) ; to quote, "Carbon was introduced in incomplete form in 2000, as a shared library backward-compatible with 1997's Mac OS 8.1. This version allowed developers to port their code to Carbon without losing the ability for those programs to run on existing Mac OS machines.") Given that Mac OS 9 was still current when the first version of iTunes was released, it made sense for iTunes to be developed as a Carbon application (since Carbon applications can run on Mac OS 8 and 9 as well as Mac OS X) rather than as a Cocoa application (which can only run on Mac OS X).
https://en.wikipedia.org/wiki/Carbon_(API)
Apple's original plan was presented in 1997. Steve Jobs announced the "change of direction" in 1998. iTunes was released in 2001.
NeXTStep (and thus OpenStep and Rhapsody) already had a file browser/desktop application unrelated to the Finder.