As so often, the problem was not in but in front of the computer :-(

Once the keys are generated (ssh-keygen) you need to share the public one with each user ($ ssh-copy-id username@remote-user-IP) AND must do this for each user using this, so in particular yourself AND root!

I may have made a typo when adding key as root, and not notice this failure, and therefor there was no key access for root :-(.

Sorry for this confusion.