With respect, this shows an ignorance of the historical role of journalism in democracy.

to cite sources

Sources may have valuable information to get out, but not be willing to go on the record. Professional journalists are like doctors in that they've committed themselves to a code of ethics. As citizens we are called on to trust them to not make sh*t up.

For publicly available written sources, it's only a bit different. Yes, they could cite every sentence they write, and indeed some do, but it still comes down to institutional trust. If you don't trust where you're getting your news from, this is a problem that's probably not gonna get fixed with citations.

make them liable if it turns out to be false

A terrible no-good idea. Legislating for truth is a slippery slope that ends in authoritarian dystopia. The kind of law you are advocating exists in a ton of countries ("spreading dangerous falsehoods", abuse of defamation laws when the subject involves an individual, etc). You would not want to live in any of these places.