The level of knowledge needed to adequately parse an expert's opinion, evaluate it, check its assumptions, research the evidence supporting those assumptions, follow up with research on the validity of that research... well, it takes a lot longer than a TV segment. In a TV segment like this, the "expert" with the better grasp on rhetoric and rhetorical devices "wins" in terms of audience agreement, and factual & verifiable basis of opinions is a distant second in terms of influence on audience agreement.
Or strike that: it's probably a distant 3rd: 1st place influence is whether or not it agrees with a viewer's current opinion. 2nd would be rhetorical ability, 3rd would be any actual evidence.
So, by all means let the facts speak for themselves-- just don't let yourself believe that is readily possible in a TV segment like those referenced.
Showing which news sources employ the most underhanded rhetorical devices may be a positive goal in itself, but it doesn't, by itself, help the audience make their own determination on an issue. Even more of an issue is that a viewer's determination of which source is more willing to mislead or omit relevant details is much more likely to be influenced by prior opinion than by the content of either source.
Basically, the problem isn't, in itself, biased news sourced, its that the format is fundamentally ill-suited towards giving individuals enough information to come to a reasonably well-supported position on just about any topic of moderate complexity. Further take any topic that appears to be of simple complexity and scratch the surface a bit and there's a decent chance it will turn out to be not so simple.
Even if putting that aside, the utility of bringing to light underhand tactics isn't meant to be used in and by itself but instead serves as one of many aspects of debate to help decide what is right/wrong true/false.
Regarding the poor suited nature of news for getting the full story across to reader I fully agree but again just because a tool isn't perfect, it doesn't mean it gets cast aside; more perspectives (and these are mainstream organisations) on a subject doesn't hurt at all.
I don't have an answer on the issue of news organizations being poorly suited here. On the one hand, there is an appeal to your the idea you convey that something is better than nothing. However, that status quo is also what has lead us to the current situation. There is a correlation with the rise of 24-hour news networks and the internet with the increased vitriolic, polarizing, and propagandist tone things. The need to fill air time was a big part of that. I don't wholly think that was the cause. There was some trend in that direction already:
Note to readers: This next part is not intended to cast blame only in one direction. It is simply one concrete example of the type of things that became commonplace.
Around 1990 Newt Gingrich penned a memo for titled "Language: A Key Mechanism for Control" It went on to explain how language could be used to manipulate people, complete with a guide for how to use demonizing dehumanizing language against political opponents. Over the years it was systematically disseminated through his party, and when Newt became house Speaker around 1995 he literally made it required reading. Shortly after is around the time that the term "liberal" went from being a fairly neutral description like "conservative" to being a hated moniker for a political opponent. (Though right-wing, alt-right, etc., fill that purpose. now for the other side)
A journalist’s job is to try to present the truth, not create false equivalence.