In an intrinsic semiconductor, why don't electrons go out from both valence and conduction bands?
If it's intrinsic, there's as many electrons in the conduction band as holes in the valence band by definition, because each electron leaves a hole.  The electrons in the conduction band are bound to their atoms by (relatively weak) electrostatic forces, and can move fairly freely.  

Electrons in the valence band are bound more tightly, and largely move only from one atom to an adjacent one that contains a hole.  

Bottom line is, all the electrons are moving to the left--some in long unfettered paths, and some from one atom to the next.  Also, in the valence band, it's kind of tag-team...an individual electron moves to an adjacent atom leaving a hole, then another electron from the other side fills that hole.  It's just as easy to model it as a hole propagating than a tag-team of electrons.