Why is a steel security door safe if they can break the glass, slide their hand in, and unlock the door?
You could just chill out.  Putting  up bars or plastic on that door is truly ghetto.

Doors like this are not inherently unsafe at all.  Your door is appropriate for your neighborhood.  Your door would be unsafe or inappropriate for a bad neighborhood or an apartment building.  Having this glass probably does not effect your chances of burglary by .0000000001%.  Having a fake security sign in your front yard would probably be a better deterant by 1000000 times vs bars over the glass.

The fact is glass next to a door is hardly ever the easiest and most elusive way for a burglar to open a door.  If you are in a nice neighborhood breaking into a house the last thing you want to do is break glass as that screams call the cops on me.  For your door I would simply kick it in if I were not going in a window or something like that.  Even with a decent deadbolt (less than 2 inches) it would be faster to kick in the door vs break glass as I can shut door after kicking it in and it looks "normal" vs what the hell is on the other side of the glass.  

The point is spend your time on something else.  You can get really good deadbolts, plastic your windows, stuff like that but that doesn't deter.  A little 6" security sign, motion activated spot lights, getting rid of bushes and limbs that hide your house, not throwing away boxes for flat screen TVs at the curb, watching who you let in your house, not leaving a spare key in your yard, and so on are far more important than your door issue.   You aren't the first person to think of this, it just isn't that important compared to everything else.