You are remarkably wrong here. In fact, live sports has come to completely dominate TV over the last 20 years. 9 of the top 10 most watched TV shows in 2016 was a sporting event:
http://www.nielsen.com/us/en/insights/news/2016/tops-of-2016...
I would argue the opposite: that "prestige" TV shows are a response to live sports by networks that don't have NFL or NBA rights.
But that diverges from my main assertion that with less time available to working people, people prefer to follow a story with familiar characters in a 1-hr window rather than have to watch a 3-hour affair between two random teams.
Now they compete with the internet. Highlights? Go to r/nba, r/soccer, r/nfl, r/hockey, boom, done, quick gif, lots of good discussion. Why spend an hour watching sportscenter? Especially now that they talk about music, twitter, and lebron james 24/7, endless commercials, always before what you spent the last 20 minutes waiting for, for something.
Not only that, youtube channels, podcasts, fans making their own content, blogs, and other forums...there's just way more content out there now than in the 90s, where all you had was the newspaper/magazine instead of the TV.
On top of that, all the major leagues have their own networks now-NHL net, NBA net, NFL net. In addition to FS1, and competing with the major networks for top events.
It's not just people watching game of thrones (those shows don't air all year around and only take up an hour a week anyway.) Although I'm sure it reduces those numbers a bit.
Just like a captivating TV series, sports demands your attention to the details and personal stories for you to become a fan. However, sporting events take hours to ingest at a time and the outcome leave many disappointed. People who have money to spend are typically people with fewer hours to allocate for entertainment. With the rise of quality TV shows that take one hour to consume, how do sports like baseball stand a chance at gaining new viewers?
The best thing ESPN has going for it are its 30 for 30 documentaries. A well produced documentary series. However, documentaries generally don't bring in huge sums of cash. If they can pivot to a create must-see dramatic show with a sports theme, they may have a chance.