The purpose of rebar behind the anchor block is to take the vertical and horizontal tension forces originating from the concentrated anchor block compression. Saint Venant's principle applies only at a certain distance into the slab; close to the edge, the compressive stresses disperse at an angle (stress distribution depends on block location and amount of blocks), leading (with one block in the mid-height of the slab or beam) to the formation of two compression diagonals (often idealized as 45 degrees, measured clockwise and anticlockwise from the beam N.A.) and a tension diagonal.
The primary issue is not the anchors "popping out from the slab", but rather a bursting of the slab and a subsequent "pulling in of the anchor block into the slab" and catastrophic failure.
PS. The anchorage rebar is usually placed before the pour, and thus, they should not interfere with the tendon ducts and tendon stressing. The area adjacent to and behind the anchorage block is concreted after the tendons have been tensioned and locked.