That doesn't really matter when the media knows that the more it reports on lurid crime, the more people pay attention, meaning the more they can charge for advertising.
The consumer of commercial news is not the customer, they're the product.
If you were right and people researched things they heard on the news, disinformation wouldn't spread. And Biden wouldn't have to say that violent crime is historically low.
I mean I have no idea why you think he would bother saying it if most people researched this stuff.
But it does matter. It matters very much that they're voting and behaving based on things that are not actually real. It matters that Biden's telling the truth, and evidence supports him. Does it mean his message is going to resonate with voters? Probably not. But it goes to the heart of our current predicament to observe that the world that exists in people's heads doesn't resemble the one they actually live in. We are in a self-fulfilling doom loop.
If we grant that crime is down but that Biden should act like it isn't down because people think it's up, then we're venturing off into a very dark wilderness where nothing is true and facts no longer matter. That's a world where people like Trump thrive.