Why aren't leading edge root extensions used on airliners?
Leading edge extensions like slats are used in airliners. Most of these are controlled ones, so as to improve low speed characteristics. 



By Adrian Pingstone (Arpingstone) - Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=4761104

The dog tooth extensions were used in some older airliners like the Ilyushin Il-62 and the Vickers Super VC-10, he reason being the requirement to reduce drag.



By Sergey Lysenko - File:Air-to-air with a Russian Air Force Ilyushin Il-62M.jpg on Wikimedia Commons, originally published on http://russianplanes.net/id164205, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=40618026

The other leading edge extensions like LERX (and even dog tooth) are mostly found in high performance combat aircraft as these increase the stall angle and improve maneuverability; these are not the typical concerns in the commercial airliners. In airliners, vortex generators are used for preventing separation at low speed (high aoa).