CS is a task to keep you occupied in the game, imagine League without it.
I think it's sort of a bait to encourage fights. Both you and your enemy are in lane, so you can get gold and exp to win teamfights and proceed to take objectives (which purpose is to win the match).
And people don't group mid to finish the game right off the bat at level 1 because they wouldn't get that far before the other enemies would come to defend, now with some gold and 2-3 levels ahead of your whole team probably still level 1.
Now, since it is meta to be on lane might aswell take that extra mile and try to harass your oponent who's tryna do the same. Instead of passively farm there's gameplay around it.
If there wasn't need to last hit for gold, there would be only exp left to be on lane for. So one would simply sit back?
CS is "easy to obtain" but not guaranteed which makes it important and the difference between elos is reflected on it