"Who's laughing now, eh Joker?"

"Yeah, why so serious?"

Such a public arrest was certainly not what Batman himself would've gone for, personally.

"Ha ha ha." The flat monotone creeping from between painted lips was positively drowning in sarcasm, let alone dripping it. The lowest form of wit was being spat at him and he had nothing better to retaliate with. So he closed his torn smile and walked in silence, head held up and poisonous dark eyes straight ahead. Dignity seemed to ebb from him as though he was parading through Gotham's main square because he felt like it, and his hands were clasped behind his back simply because he wanted them to be.

Apparently this was authority making an example. If they could catch the Joker, they could catch anyone.
The public didn't need to know that it had all been the work of the Dark Knight.
Not forgetting that the Joker practically handed himself over with all willingness.