This is what sports twitter is. Yes, you have to build up the list of people you follow and interact with people to build your followers, but I would much rather that than have to share a sporting event with every fan. I would rather have the content and the discussion separate. This gets even more important when something is a global (such as a Barcelona - Real Madird game). Everyone can join the dicussion and you can curate it to your preferences. I can only imagine having a chatroom with a half-billion (or more) people in dozens of languages. Sports also has the built in advantage of being the one thing most people will consistently watch live and is (typically) broadcast live across time zones. People also expect for results to be "spoiled" if they didn't watch live and know they are responsible for actively avoiding that information. Essentially, sports are (IMO) the last form of entertainment that dictates what time you watch.
I am convinced I love twitter as much as I do because I use it primarily as a way to watch and discuss sports with other people who love that team/sport/game as much as I do. Even among my real life sports fan friends, our interest in a particular game or sport differs. Not so much those who are actively watching and commenting on the games on twitter. You are there and engaged because you want to be. Due to this, I was able to meet fans of my teams that live in multiple countries and consistently talk to them, even outside of that particular event. Especially for sports, so much of the interaction happens arounds the games (who to play, who to sign, tactics, etc.). I would hate to only interact with people in that small time frame and miss all surrounding discussion from people whose opinions I find well thought out or think in a similar manner that I do.
The short snippets of text are great for getting stats and updates directly from reporters/teams/leagues, too. Highlights are able to be immediately played via twitter and photos, gifs, and screenshots are immediately shared. The NBA has really embraced social media with its content policies (cannot use more than two consecutive minutes of broadcast footage without a license; 20 minutes of spliced highlights is fair use) that lets fans make mix tapes, instant highlights, gifs, etc, easily and without fear of copyright takedown notices. In turn, the NBA essentially gets free marketing from its fans. This is where the NFL really blew things, even locking down offical team accounts. Teams are starting to use Periscope to broadcast press conferences, interviews, and warmpus to their fan bases.
If you want to see this kind of dynamic live, check out a big game or a night with a lot of games on NBA twitter. A good-ish place to start would be the SB Nation accounts for the teams and who they are RTing and interacting with. It can be a whole lot of fun and it is easy to catch the highlights of the other games or know if someone is having a monster game you should switch over to.
To me, the wider web of people that twitter catches is much more appropriate for these types of interactions than facebook ever will be. If your goal is to have your small group of friends watch a show, I can see where you find current offerings lacking. But when you want to get involved in an existing "event" twitter is really great for that.