To the comedy point, I think right-wing satire is just hard to make happen. The idea of satire is that it (metaphorically) lobs a brick through the window of large institutions like governments and corporations, and the people who run them. Because the people who run them tend to be right-wing, there's less incentive to throw the brick, because chances are it'll land on your own foot.
If you see right-wing politics as based around the idea of protecting and preserving what already exists, again, the concept of maintaining a status quo just isn't funny.
And because the right-wing is seen as the ones with all the money, a right-wing comic poking fun at the left would have to be exceptionally skilful not to come across as spiteful and mean.
Also, I think when you say 'right-wing comedians' people tend to think of old-school sorts like Jim Davidson, Roy 'Chubby' Brown, Jethro and so on. Those acts are not only offensive - although I did enjoy Roy 'Chubby' Brown satirising himself in League of Gentlemen - but the style is hopelessly out of date. Maybe the production bookers are nervous about putting right-wing comedians on panel shows because they worry there will be off-colour jokes about race, women, gay people...
To news media... I think the idea of bias in media is sad, full-stop. Once upon a time people watched the news for the facts. Now they select their media source based on who is going to spoon-feed them the warm diarrhoea that's most like their own, whether that's the Daily Mail or the Canary.