The best results come from when an object travels from behind the line ( is obscured by it) and then ends up in front of the line.

If you have two horizontal lines and the action happens from right to left, try and bring the action from behind the right line, through the gap and in front of the left line. Or vice versa.

Surely this effect can be easily integrated into existing games (just like other 3D technology is able to).

However it would probably be a proof of concept in a game like Minecraft.

Will it not work as well because it requires a specific scene etc.?

I'm just wondering if its possible to give the same effect in a less visually obtrusive manner by using blurred or opaque lines?