The Western is a dead genre right now so no they wouldn't make a Western TV show.
However, the popularity of genres increases and decreases in different periods of time. Westerns will be back at some point in time.
An 'episodic' Western would probably and hopefully get laughed off of TV though. Nowadays they need to and should include character and story development in a series.
The classic Western is a racial mythology. Integration finished the classic Western, though it took television, a very reactionary medium, some years to notice. No modern Western can get away with reducing the native Americans to savages joyfully slaughtered
That's an excellent point. That certainly would make it harder for not-so-talented writers to write a good Western nowadays than it would be for similar writers to do so in the past.
However, I'm sure they could still get away with portraying Cowboys vs. Indians in a war situation by doing it in a non-racist way. Just because it hasn't been done before (AFAIK) doesn't mean that it cannot be done.
Failing that, they could always leave it as Cowboys vs. Other Cowboys.