I can tell you from personal experience that the unanimous requirement for jury verdicts is frustrating. I once sat on a jury in an attempted murder case, and we were in deliberations for three straight days, with 8 voting to convict and 4 voting to acquit, and nobody would budge. Finally, the judge declared a mistrial, and all of our efforts and time away from work and family (about two weeks) accomplished little and another trial was ordered.
Despite that frustration, I do believe in the unanimous jury verdict. In a criminal case that actually goes to trial, we are talking about a person's freedom or a victim's sense of justice. I think it pays to be as sure as humans can be that they are convicting the right person, or acquitting them forever of that charge before we send them to jail or set them free, and the collective wisdom of the group of twelve regarding the evidence minimizes the personal agendas and biases of any one of the twelve. If, in the end, we can't be sure, then it is best to give another group of 12 a shot at it.
Convincing all 12 jurors also puts an added requirement on the police and prosecutors to do their job well and within the law, which safeguards the rest of us as well.