As far as 'the other end' it is not the player but the PUCK that must cross the center line to avoid an icing. In the same respect as an offsides call, the center line is considered 'neutral space' in that on the way out of the defensive end, if the puck is let go on the red line it will be icing, but if the puck is cleared back to (but not over) the red line and then iced, it will NOT be an icing even if from the exact same spot. The blue line works like this for offsides; you have to completely cross over the blue line to enter the zoen on sides, but the puck has to go all the way over the line to be out, as well.
Touch icing is not the problem. The problem is that the league fails to penalize players who act dangerously and outside of the rules on icing plays. If the league properly penalized them, you would never see injuries from contact on icing plays.