When Weiner's anatomy became a national story, House Dems weren't dealing with some back-bench nobody. He was a proxy for the leadership. All of his TV appearances and interviews weren't only because he was good on TV and bookers liked him, though that certainly helped, but because there was implicit sign-off from the leadership.
That's not the only reason Weiner had to go. There were other reasons, political and personal, that made it unlikely Weiner could survive what might have been the most boring sex scandal DC has ever seen. Unlike David Vitter or Bill Jefferson, who had no national visibility when their scandals hit, Weiner was actively being put forward into the limelight as an semi-official national spokesperson. Their fresh face turned out to be way too fresh.