Do you think so? I'm not sure I agree. It's useful from time to time but generally you need an overview of everything going on to understand a game. F1 has had this for a while (each weekend you can select from several cars to view live, onboard footage for the entire race. Just watching that you have no idea what's going on overall and it's quite boring. A picture in picture scenario is more useful.
It probably depends greatly on the sport. American Football seems particularly well suited to first person speciation, given there are only about 11 minutes of actual gameplay in a 3 hour broadcast - there is already a lot of detailed replay after you've seen the bigger picture. There are also lots of individual sports where the big picture isn't as important to understanding what's happening, where a mix of first and third person sounds pretty exciting - skiing, maybe tennis if it isn't too disorienting, for example. And some team sports have predictable moments where the big picture is not necessary, like the pitch and swing in baseball.
Plus, if first person is compelling enough, sports may adapt to be a better fit, especially if they suffer from competition with sports that are already well suited to that type of spectation.
It could make for interesting cutaway shots or PIP, but as you said, it would only be useful from time to time.
Previous footage I have watched of football players (American) is very disorienting, and the field of vision is very narrow with a helmet mounted camera. It looks like the player has tunnel vision. However, a player's eyes will dart back and forth very quickly taking in a much bigger picture, so you aren't really seeing what they are truly seeing.
The Madden video games implemented a first person perspective (I haven't played for a long time, so not sure if they still have it), and it was nearly impossible for me to play in that mode. You don't have any peripheral vision using that mode, and that same problem will exist for these live sport shots.
I think this depends on the game. You could probably watch 90% of a tennis match from a single player’s viewpoint and not miss much. The other issue is how well you can switch views. Basketball is probably way to fast paced, but you could watch most of a baseball game from a pitchers viewpoint, and only switch to the overview after a big hit/bunt etc which takes long enough that a camera operator can easily follow things. Stealing bases which is normally a fairly borning part of the game would also be much more interesting with a more limited view.
Football would be somewhere between those extremes.
Hockey probably works well from a ref's viewpoint as they try and watch the action, but stand far enough back to get decent coverage.
You certainly wouldn't want to watch the whole game that way, but it can make for some interesting replays. When the player made a terrible or great play, it could quite a bit of insight to see the game the way that they saw it.