Unpopular Opinions
Honestly?
Yes.
While I love watching the real dynamic duo here, honestly speaking there's no value to keeping one psycho alive at the cost of thousands of innocent Gothamites.
He's obviously not curable (and I'm an HQ fan, but still) and he's obviously not above killing others indescriminately himself.
If I have to put it bluntly, I switched from reading Batman to reading Red Hood a long time ago; partly because unlike Batman, Red Hood (the former second boy wonder who Joker literally KILLED) understood the idea that not everyone is redeemable, and that sometimes it's more honorable just to kill the bad guys than continue to allow your mercy to be someone else's repeated trauma.
.............
Now, this is running under the assumption we're talking about the new, dark, gritty Joker & Batman and not the original slapstick 60's ones. If we were going back in time on that then absolutely not, there's no excuse for taking Caesar Romero out, he's legendary.