The Last Conformist is right. As far as realism is concerned there are only three explanations for what a "unit" and "killing" it mean:
1) Unit is a single figure: both artillery and other units definitely can finish a single figure off.
2) Unit represents a group of figures and "to kill" means to completely destroy: neither artillery nor any other unit can kill the group.
3) Unit represents a group of figures and "to kill" means to break the group to the point of rout/surrender/immobility: both artillery and other units can kill the group.
From the real world point of view the non-lethal civ bombardment is inconsistent no matter how you define the concepts of "unit" and "to kill".
However, however: This is one of those cases where realism has to bow before the Mighty God Of Game Balance. If you allow lethal bombardment (with other game rules staying the same!) then the game is rendered to a meaningless and dull artillery duel if it's a multiplayer game and to a foregone (and dull) conquest victory in a single player game.
The AI can't handle lethal arty at all and humans OTOH are too good at it.
I am not saying that lethal bombardment couldn't make the game better. Only that if it's included then something else has to be changed, too, to balance things out. What that something is I don't know, though.
Maybe one solution could be that artillery could be flagged lethal to all "non-foot units". This way you could sink ships with bombarbment, massacre cavalry, and destroy tanks (all things that real world artillery has done) but entrenched infantry would at most be reduced to 1hp. Because unless you nuke them (and even that is debatable) the only way to defeat an enemy infantry division is by sending two or three of your own to dig them out. Artillery only makes them keep their heads down.
But like I said, unless the AI can be made to handle lethal bombardment even the above "non-foot" rule is too much power for the human. Possibly could work in a multi player game, though.