Yes, the problem is they didn't get enough viewers. Lots of reasons for that. The people who are going to care about high-quality journalism and not care about the negative connotations of an Arabic ownership are less likely to subscribe to cable, the only place to find Al Jazeera. Conversely, the majority of people who watch cable news tend to be older and more conservative, which is why Fox News has the number one viewership among cable news channels. Most people who watch Fox News will fit into the xenophobic demographic I mentioned above. If you don't think the "average American" (in this case "American" is defined as "someone who watches American cable news channels", not actually the average American) is that closed minded, remember that in 2012, Fox News had 2 million viewers compared to CNN's >700,000. Fox News has more viewers than every other cable news channel combined. [1]
It's not necessarily about the language, it's about the connotations. If you watch Al Jazeera, you're watching the terrorist propaganda. To the majority of people who watch cable news, that's where the thinking ends. You're right, it's not healthy, it's destroying our nation and the entire world with it.
Liberals are going to be pretty happy with NPR. Younger people are going to get their news from social media, not from cable. Conservatives are going to be very happy with Fox News. Older people aren't going to want to switch their news channel to something unproven. Al Jazeera has no audience in the US if they're trying to break into the cable news market.
[1] http://press.foxnews.com/2012/12/fox-news-channel-dominates-...