Juror fined $11,000 for doing research on a case, despite being instructed not to

I think part of the problem here is the "all or nothing", "black and white" nature of the trial system. "He either did it or he did not"

In my personal opinion, if a defendant is suspected of carrying out a bank robbery and the evidence isn't the most solid, but they have a history of multiple previous bank robberies, then they should be punished for that crime, but not punished in a way that assumes they certainly did it.

If what we have is only a probability rather than a certainty, then the level of punishment should be accordingly.
(Not a linear relationship, but some more complicated mathematical connection)

 

They should be punished for a crime that they didn't commit?

 

I think what you actually mean is "they shouldn't be punished for a crime that there is a big enough probability that they might not have committed.

Nothing is known with absolute 100% certainty.

You are expressing your belief that they should not be punished if the level of doubt is high enough.

You also seem to believe the jury cannot be trusted to do this, so you believe certain facts should be withheld from them that could be likely to lead the jury to make a wrong decision.
Even though those facts may not be entirely irrelevant.

If a defendant has been convicted multiple times in the past of bank robbery, and is now being accused of bank robbery again, don't you think that is a factor the jury should consider? Alongside weighing it with all the other evidence.

By the way, it's not that I believe anyone should be punished for a crime they didn't commit, but rather I believe the jury should have some input about making sure the accused is not punished too much when the evidence leads them to vote guilty but they still believe there is enough doubt about whether the accused might be innocent.
People WILL vote guilty when they are not absolutely certain. It just simply would not be practical to do otherwise. Very rarely can a jury ever be completely certain about anything. You are just being naive if you do not understand that.