I was experiencing the exact same issue during the last couple of weeks and decided today to do something about it.
As you correctly say, an internet (or SE) search only gets you solutions valid for older versions of Windows. I still tried several of those, including:
- Delete desktop.ini
- Delete the iconcache.db file in appdata/local
- Delete all iconcache_* files in appdata/local/Microsoft/Windows/Explorer
- Most of the commands to reinstate corrupted Windows system files, including an in-place upgrade using the media creation tool
- Reinstall newest graphic card drivers and carefully go through the configuration
I even had a 2 hour support session with a technician from Microsoft. After confirming that there is no quick solution, his first idea was to install a third-party app to block the desktop icons in their position which, like yourself, I didn't want to.
He then noticed that the problem does not appear in a newly created user profile. So his final advice was to just transfer all my files into the new user profile. I probably don't need to tell you that this would have been a real pain to do, seeing as how I would have to manually select which registry entries to take over to the new user. All that just to stop the desktop icons from acting up?
So I kept looking and exploring. Since no fix was available, I tried to better understand where Windows stores the desktop icon positions and came across this helpful SE article: Where does Windows store icon positions?
It explains how Windows (starting with XP?) seems to store icon positions depending on resolution in registry entries under HKCU\Software\Microsoft\Windows\Shell\Bags\1\Desktop. So, by deleting the DWORD values starting with the name ItemPos, you might be able to force a reset of your Desktop icons if the other solutions I mentioned above don't work.
This did not work for me, though. But I noticed a binary value called IconLayouts in the same registry key, so I researched this further. It seems that this value was only introduced with the Creator's Update, i.e. Windows 10 Version 1703. (Source: MS Technet Forum)
Deleting the IconLayouts value finally solved the issue for me, I can now arrange the icons on my desktop to my liking, and they remain even after a restart.