Sure, why not? They have a blank checkbook funded by taxpayer dollars - just as the Founding Fathers intended!
Oh, wait...
I have to agree, they can retry til the resurrection, doesn’t cost them anything, the citizen in the cross-hairs however has finite resources, and they know it. I think there should only be two options available to jurors, guilty or not guilty. Not 1)guilty, 2)not guilty, and 3)we couldn’t decide. Since you are presumed innocent, if you can’t convince 12 people that they are guilty, that should be it. No more bites at the apple, double jeopardy attaches.