I'm, not sure why you think there is horrible fringing. When used correctly, artifacts are hardly noticeable when studied closely on single images and practically invisible when viewed on the move. Like I said before, Fake DoF is currently used the majority of time in VFX over in-camera DoF because it provides a better result for less computing power even if the trade off is some tiny artifacts here and there.
Plus, Foreground/background issues with fake DoF are even less of an issue when using a good pixel filter, like 'closest to camera', and with Deep rendering slowly becoming more popular, fake DoF is almost indistinguishable from in-camera DoF.
Below is before and after fake DoF is applied on a shot I am working on that has an obvious foreground and background.
[Edit:] Just for perspective, the last 5 projects I have worked on (X-Men: Apocalypse, Game of Thrones, Gods of Egypt, The Wolverine, X-Men: Days of Future Past) we never used in-camera DoF, but plenty of fake DoF.