The legacy media business hasn't seen an IPO for a very long time. Instead the big trend is the other way around: public companies being taken private.
The big success story is the Washington Post, which traded under the ticker symbol WPO before it was bought by Jeff Bezos for $250 million. Under his aegis, investments no longer need to generate an immediate improvement in the bottom line. The result is a revitalized property that's almost certainly worth much more than Bezos paid for it — were he to want to sell it, which he doesn't.