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.