What for? Or was the maniac hiding at home to set someone up? I don't believe it; there's no benefit for him. Because if the maniac isn't caught and the evidence points to him incorrectly, then he has nothing to fear when killing. In any case, the evidence is too complex to decipher.
So, executing the useless "What?" is not beneficial to the city.

Added 1 minute later
I think they were actually killing the Terminator. They didn't even touch Jack; he became like a random witness.
By the way, Sparrow is a cool guy; he SYNCHRONIZED with his ND.