1) By and large, people are at ease with shooting carbons because ignorance is bliss. That encompasses probably 25% of the bowhunting only, carbon shooting community. Now, there is another 25% that is smart and careful enough to never shoot at the same spot twice. If your arrows are not impacting a hard target, then the chances of something major happeneing are very remote, especially if you check your arrows before each outing. If you hear a crack, or your nock flies out of your arrow upon target impact.... then you need to carefully check that shaft and perhaps even disgard it in the name of precaution.
2) Quite simply, every time I drive could be the last time as well. I still think archery is safer than recreational driving.... road accidents being the leading cause of accidental death in the US.... by a good margin too. When you are careful and take precautions, your odds improve drastically regarding the arrow issues you are concerned with.
3) I've worked professionally in the archery industry for almost 7 years now. I have only ever personally seen one arrow that completely broke on the string at release. And at that, I didn't see it happen. It happened at our range while I was at work. The shooter, a good customer of ours and avid archer, had a nasty bruise but was other fine. Lucky perhaps. He wasn't entirely sure what caused it.
4) If you are not comfortable shooting carbons... then don't! Archery is supposed to be fun and enjoyable. Safety is always first. If your safety meter is running in the red shooting a carbon, I'll tell you personally that an aluminum will punch the X or kill a deer everybit as dead center and stone dead as a carbon will.