A couple battle ships within 10 miles would have been blown out of the water. The amount air cover needed to keep those battleships safe would go up a lot for ever mile closer to the enemy concentration. In their back yard we would not have been able to keep the diver bombers off them.
Word was passed to Alexander, at the top of the command chain, that the Axis forces were trying to withdraw. The air commander, Tedder, committed to bombing the straits upon command. Cunningham, the naval commander would commit to nothing, other than he ‘would give the matter careful thought.’ In the end, Alexander gave no orders to intervene.
As I understand it, the Allies had air supremacy more or less throughout the Battle of Sicily.
The accounts I’ve read indicate that surrounding the island by occupying or interdicting the Straits just seemed to slip everybody’s mind till pretty late in the battle.
http://www.airpower.maxwell.af.mil/airchronicles/cc/renner.html
A LOT of Axis forces got away, somewhere in the vicinity of 125,000.