Essentially, people are only willing to pay for "news" with which they are in accordance. Whether or not a particular news source is factually accurate, is very much a secondary concern. (Witness Bloomberg.) So you generally have two huge markets, one for "news" with a conservative bent, the other for "news" with a liberal bent.

Of course you have several markets, that are much smaller, for other types of "news". But very few markets where factual accuracy is at a premium. Add to that the fact that the few markets where factual accuracy is at a premium are small, and it's not hard to see why no one really caters to them. (All of that doesn't even consider the very real problem that it's hard to address such markets with a product that those markets would accept).

So pointing out the inaccuracies in Bloomberg, or CNN, or WSJ, or NY Times, etc misses the point. These media companies are in the business of selling "news". They don't put a priority on the business of selling accuracy because the business of accuracy doesn't really pay very well.

Think of it this way, you likely know a lot of people who consume, say, FOX or CNN, but how many people are you acquainted with who watch C-Span?