Yes you can install the OneNote 2016 application, a "real" application, not "new & improved" <sarcasm> windoze 10 <cr>applet.
The problem is that MS is no longer developing the OneNote 2016 application. They will not add any more features to it. In a few years it will fall off the map and we will only be stuck with the UWP version.
Here is the MS propaganda about this "improvement"
OneNote 2016 is missing after installing Office 2019 or Office 365 – link to manual install
https://support.office.com/en-us/article/onenote-2016-is-missing-after-installing-office-2019-or-office-365-1844ba87-7248-4bd8-a735-66a52f98e6e5
What’s the difference between OneNote for Windows 10 and OneNote 2016?
Here is the first paragraph from the above link:
<snip>
OneNote for Windows 10 (simply labeled “OneNote”) is the best and most up-to-date version of OneNote on Windows. It was designed to feel natural with any input method — from mouse and keyboard to pen and touch — and it contains numerous improvements for
better performance, battery life, and reliability.
</snip>
Once you pick yourself up from the floor, ROFLMAO, read on ...
The very bottom of the page has a link to the OneNote uservoice feedback page
!!!USE IT TO SUMBIT FEEDBACK!!!
The comments made here are not being seen by MS management. Submit your complaints directly to MS using feedback, or vote for existing feedbacks, and add your comments to existing feedbacks.
UserVoice: Include OneNote for Desktop in Office 2019
https://onenote.uservoice.com/forums/327186-onenote-for-windows/suggestions/32737648-include-onenote-for-desktop-in-office-2019
Learn more about the future of OneNote.