Indeed, but it's up to the defense to articulate what the basis of that doubt is. If you read jury instructions, they typically tell the jurors to only base their decision on the information presented in the courtroom and to set aside their own intuitions, prior life experience etc.

Now this isn't universal; I've seen judges that encourage the jury to ask questions in open court (by submitting as notes to the judge who reads them out), for example. But that's very unusual. Judges who make a habit of questioning submitted evidence are likely to have their rulings challenged far more often and be accused of bias, even if they are superb jurists. And high status in the legal world goes to appellate judges whose rulings set legal precedent. Trial judges do get cool points for calling out bad lawyering and writing spicy opinions but this can also be a career anchor.

We are encouraged by civics classes and media to believe in courts as truth-finding institutions, but the reality is that most of the time they are engaged in argument-scoring. Even to the extent that they do pursue truth via the appellate process, it doesn't happen in a timely fashion. There's saying that the wheels of justice grind slowly, but they grind exceeding fine, which goes back to the Roman empire: so you're looking at an institution that is historically so confident in its process that it has become divorced from any sense of urgency in its application.