Why would you ever want to intentionally miscue?

Here is a situation that comes up every so often: The only object ball that you can hit is so close to the cue ball that you can't hit it without fouling by pushing, or hitting the cue ball twice with the cue. (Cue "A")

The answer is not obvious but is easy: Intentionally miscue.
1) take the chalk off the tip of your cue
2) aim at the extreme outside edge of the cue ball, away from the object ball (Cue "B")
3) lighten the grip on your cue.
4) stroke it fairly quickly.

The tip of your cue will hit the cue ball, sending into the object ball.
Simultaneously, the cue will miss cue and will fly away from the cue ball.
When the cue ball rebounds from hitting the object ball, your cue will be a safe distance away.

So you struck the cue ball once, and then the cue tip bounced off the cue ball in a miscue.
The cue ball legally struck the object ball, without pushing.