Thanks Diegator: I think it could be an asset to have a tilt that is not noticeable. It's like watching a movie with music that you did not even notice...That is when music is seamlessly integrated.
The best tilts don't have to make you aware of the tilts in a composition. It can be a subliminal enhancement. They don't always need to be in-your-face. Often, I find tilted shots obnoxious, because the tilt is too extreme for my eyes...and for my neck.