@Kierlak Batman is a symbol, not just a hero - the entire point is that he already works "outside" the law. He's in the morally grey area where his own crimes technically aren't egregious enough (stuff like breaking-and-entering, assault and battery, etc.) to the point where it would necessitate his arrest, since he, overall, does more harm than good by simply existing. Just like the gun of a criminal puts fear into the hearts of the innocent, the bat puts fear into the hearts of the criminal. The moment he kills someone, though, is the moment the "vigilante" excuse is thrown out the window - self-serving justice through death is basically just murder in the eyes of the law.
As a side to that, the point of the Joker is that he's doing all these terrible things because he
wants Batman to kill him, proving once and for all that anyone can be corrupted to become just like the Joker - all it takes is
one bad day and you're no better than he is. The Joker knows that there can and will be someone (or some
thing) worse than himself that can terrorize Gotham - and it doesn't even have to be a criminal. Harvey Dent is a somewhat good example of that, as is Hush - respectable folk that become corrupted by something. Kill the Joker, then what? Kill Freeze, Cobblepot, Ivy, Dent... but then where do you start drawing the line? Common thugs, sure, murderers, thieves, purse snatchers? Lying, greedy politicians, corrupt officials, but what of higher society? The Court of Owls?
TL;DR If he starts killing, where does he draw the line?
Real TL;DR:
If he kills, his villains would be gone, especially popular ones like the Joker, and you would need to keep making more villains for his comics to exist lul