Hung Jury is No Answer?

I agree.

In essence, a trial that ends with a guilty verdict is one where the jury says that the prosecution proved its case. And a trial that ends with a not guilty verdict is one where the jury says that the prosecution is not able to prove its case. In both cases, the outcome is supposed to be obvious.

If there’s a hung jury then the outcome wasn’t obvious. So neither the prosecution or the defense did a complete job. The other possibility is that the outcome was obvious but one or more jury members refused to admit it. In either case, the trial needs to be redone until the correct outcome is obvious and accepted.