I'm not sure why you think the police hunting Batman is a scary and odd sentiment....

You do know what a manhunt is, right? Particularly when the suspect is a known murderer of a notable public figure such as a District Attorney, which is what Batman wanted himself portrayed as.

When Gordon says "we'll hunt him," he's referring to the police issueing a manhunt for a murderer, which would be out of his hands at that point. He knows Batman's innocent, but he can't tell anyone else and he can't call off the hunt of a high profile murder.

"He can take it" means Batman can bear the burden of being seen as a monster, he can carry the load of working alone with minimal help and the police being against him. Because it's better than the alternative of the people losing hope in the justice system and Gotham completely breaking down more than it already is.

While that may be true, it still doesn't fit Batman as a character. Superman's existence does not create the probability of annihilation, his turning against humanity does. So everything we see - the sonic cannons, the Kryptonite spear, the preparation and planning, is all in line with Batman's methodical approach of contingencies for every scenario, but he wouldn't implement them until there was some sign of the event occurring. He'd be prepared for the eventuality, not commit premeditated murder to ensure the eventuality can't occur.

And it adds to the completely irrational setting where Batman will murder on a possibility of a future event, but lets Joker & Harley live.