Well, Arkham City, though awesome, isn’t technically canon material either. I think Bruce (or at least a well written Bruce) shows some manner of compassion to all the Bat-villains. But I don’t think that equals romance.

But let’s entertain the idea of JokerxBatman for a moment. What does that mean for the character, exactly? Well, for one, Bruce would have to either forgive or ignore the fact that Joker has murdered his second Robin, Jason Todd, crippled Barbara Gordon, kidnapped Jim Gordon, killed Sarah Essen Gordon, kidnapped his son, Damian, captured the entire Bat-Family and subjected them to a weirdo mind-fuck where he pretended he cut their faces off, and spent innumerable years torturing him and causing utter havoc in his life and in his city.  Batman would need to forget the hero schtick and willingly lay down with a murderous psychopath. 

Seems impossible to me that the man who’s committed his life to justice would be able to bury those feelings completely and shack up with his nemesis. 

I’m not saying you can’t enjoy the pairing. Folks are allowed to like whatever ships they like! I’m just saying I don’t personally buy it.