I don’t think it’s true that it only takes one to stop justice from being served. If one juror disagrees with the other 11, the result is a hung jury and a mistrial, and the prosecution can retry the defendant.
I would be interested in knowing how often trials with a hung jury are retried. Presumably if it goes that long and is that contentious there is a fair amount of resources that have already gone into it, would the state look at it as a sunk cost? Are they more likely to retry a case hung on 11-1 as opposed to say 8-4?