I don't know if humans are able to ignore evidence they have heard outside of court. We are not good at only including one set of information when making judgements.
I agree that free speech has significant value and restrictions should only be put in place when required to uphold other rights.
I'm sure you're not alone in your opinion that a jury is able to ignore what they've heard about a case in the media. However you do disagree with the current judicial system of most developed nations. That doesn't necessarily make you wrong. I think there is merit to the argument you're making, I just am not convinced that people can ignore information like that.
https://juryanalyst.com/blog/the-power-of-media-coverage-how...
https://www.canlii.org/en/commentary/doc/2019CanLIIDocs2798#...