I've been in the TV and radio business for a long time. Never, ever, ever has a Network executive cut or kept a show simply because of their own personal taste. They wouldn't have a gig very long if their own taste dictated what shows stayed or were cancelled. Just like radio; if the show pulls-in good revenue or associated in-demo ratings, they loved the show because that's their job. Now a Rupert Murdock-level executive might push to keep a certain host on longer than research shows they should, but that's an expense gamble their willing to take thinking of a long-game approach. Sean Hannity comes to mind.
But they kept it for many seasons didn't they? It wasn't until the series started to drop in revenue and ratings that it got cancelled.