I can't exactly figure out why baseball has a problem attracting younger fans, and the point you made about doing other things while the game is on is part of the reason why. Aren't millennials supposed to be all about trying to do a bunch of stuff at the same time (e.g., have the TV on, be on your laptop with 7 tabs open in a web browser, be texting people on your phone, etc.)? Baseball is a sport tailor made for being watched like that.
They'll say stuff like the games are too long, but I think that is BS because CFB and NFL games are longer. They say there are too many games, but the schedule has been at 162 games since 1962 and was 154 games before that (back to 1920), so that sounds like BS too; plus there are NBA games on every night and it doesn't hurt its popularity. They say there is too much dead time between plays, but the average NFL game has only 10-11 minutes of actual game action. Baseball probably has less, but I bet it is not dramatically so.
What exactly is the reason? Is baseball just not culturally "hip" enough? Does the league not do a good enough job of marketing its stars, of which there are plenty? Does the game not play well on social media for some reason? Does it have the feel of a game from a bygone era? If so, why?
I say this as a millennial myself but I can't figure out.