Scientists have to list all the sources they use. And they quickly get called out for doing mistakes in that regard and suffer a loss of trust in their work.
What would happen if everything politicians say or write had to contain sources?
Speeches are prepared anyway, so you have to publish all the sources of your speech right after you held it. Saying things differently than in the source would be illegal.
I think it would be quite interesting, and a completely different way to do politics.
I suggest googling reproducibility/replication crisis or Francesca Gino or have a look at RetractionWatch. I wish your portrait of scientists were true but alas.
If it were such a wide spread issue, then science would not achieve the results it does. It lives from people checking other people’s work and arguing about the results.
There is still an issue of human bias, though. A thought is not accepted unless it’s widely accepted. Even much of our established science was once a pipe dream, even with reproducible proof, until it was accepted on a wider scale.
It’s not as simple as just providing proof and letting people accept it, you have to appeal to them. Which is exactly what politicians do.