In-ear monitors do eliminate room variability. That's one less thing to worry about and that gives you a huge touring advantage. You get the same consistent sound, night after night, show after show.
Rob Hammersmith, drummer for Skid Row, says it best. "I was always chasing consistency and more control with onstage sound. Moving from room to room, night after night creates an endless list of variables that affect what we hear. The transition to in-ear monitoring is the most significant step any musician can make in eliminating many of these variables and gaining control over your environment."