Wouldn't you have to be in pretty deep trouble for a city with three cubes already to get drawn from the bottom of the deck (as it does for an epidemic)?
Moderate to deep. That would mean that neighbours to that city had outbreaks 3 times in the game. If those are your only 3 outbreaks, you're just half way to losing.
Since you know that city isn't in the draw deck danger area, you tend to ignore it (until it's a 3 cuber). IE, you'll remove cubes from the cities you know are at the top of the deck before you get to it.