Hi,
I'm not a Microsoft Dev, so I don't exactly know why it happens, I just know that it does...
I had multiple people attempting a similar operation and having to reinstall windows. It's simply a bad idea to modify every file on the file system. Windows doesn't like it.
Taking ownership messes with file metadata. Modifying it could cause things like certificates to not work properly anymore, but not sure about that.
It breaks things like the Windows UI (Start, Search, etc).
The broken recycle bin is already a problem caused by the process.
The safeguards are there for a good reason and shouldn't be ignored. If you want to modify files, you should change the permissions on those individually. Do this at your own risk. Modifying critical system files can render your system unusable.
It is very possible that starting the process could already have created problems. If you run into issues, probably the only way to restore the system to its original state is to reinstall windows.
If you want to have these permissions, you can check how to run CMD as TrustedInstaller and gain system level privileges that way. I don't recommend it though since you can easily break your entire windows installation that way.
What files are you trying to modify? Typically, you don't need to modify files that are protected by these levels of permissions.
If you want to modify things like program files, you should be able to simply click "continue" when a warning pops up.
Since your files already got modified, I would suggest running the following commands in CMD as admin to repair some of the damage:
dism /online /cleanup-image /restorehealth
sfc /scannow
Regards,
LightJack