Hezekiah concentrated his defense outside Jerusalem on two sides: the passes to Jerusalem, especially those near the border of Samaria (Gibeon+Mizpah), and the three (four?) fortified cities in the Shephelah (Beth-Shemesh, Lachish, and Azekah, and possibly Socoh). He did not concentrate his defense on the Beersheba Valley. Why? Because Sennacherib had a purpose for taking over Gibeon, Mizpah, and the Shephelah. He did not, however have any clear purpose for taking over the Beersheba Valley. Why? Because the Shephelah made Judah far too politically influential in Philistia for Assyria to allow, and, more importantly, it could be administered by Ashdod and Gaza. Mizpah and Gibeon could be used to stop trade coming to Judah from the Assyrian provinces in the North or be used as springboards to take over the southern part of the province of Samaria. Both could also be administered as unfortified cities within Samaria. The Beersheba Valley, meanwhile, was a vital trade artery, offered very little threat of political influence in Edom or Gaza, and could not be competently administered by any polity except Judah. Exiling the population of the Beersheba Valley would, as Hezekiah likely reasoned, be the last part of Judah Sennacherib would want to attack.
Of course, the Assyrians did end up destroying the Beersheba Valley, probably as a make-work project for Judah, to keep it from growing too strong again any time soon.